Tag Archives: quantum field theory

Amplitudes Papers I Haven’t Had Time to Read

Interesting amplitudes papers seem to come in groups. Several interesting papers went up this week, and I’ve been too busy to read any of them!

Well, that’s not quite true, I did manage to read this paper, by James Drummond, Jack Foster, and Omer Gurdogan. At six pages long, it wasn’t hard to fit in, and the result could be quite useful. The way my collaborators and I calculate amplitudes involves building up a mathematical object called a symbol, described in terms of a string of “letters”. What James and collaborators have found is a restriction on which “letters” can appear next to each other, based on the properties of a mathematical object called a cluster algebra. Oddly, the restriction seems to have the same effect as a more physics-based condition we’d been using earlier. This suggests that the abstract mathematical restriction and the physics-based restriction are somehow connected, but we don’t yet understand how. It also could be useful for letting us calculate amplitudes with more particles: previously we thought the number of “letters” we’d have to consider there was going to be infinite, but with James’s restriction we’d only need to consider a finite number.

I didn’t get a chance to read David Dunbar, John Godwin, Guy Jehu, and Warren Perkins’s paper. They’re computing amplitudes in QCD (which unlike N=4 super Yang-Mills actually describes the real world!) and doing so for fairly complicated arrangements of particles. They claim to get remarkably simple expressions: since that sort of claim was what jump-started our investigations into N=4, I should probably read this if only to see if there’s something there in the real world amenable to our technique.

I also haven’t read Rutger Boels and Hui Lui’s paper yet. From the abstract, I’m still not clear which parts of what they’re describing is new, or how much it improves on existing methods. It will probably take a more thorough reading to find out.

I really ought to read Burkhard Eden, Yunfeng Jiang, Dennis le Plat, and Alessandro Sfondrini’s paper. They’re working on a method referred to as the Hexagon Operator Product Expansion, or HOPE. It’s related to an older method, the Pentagon Operator Product Expansion (POPE), but applicable to trickier cases. I’ve been keeping an eye on the HOPE in part because my collaborators have found the POPE very useful, and the HOPE might enable something similar. It will be interesting to find out how Eden et al.’s paper modifies the HOPE story.

Finally, I’ll probably find the time to read my former colleague Sebastian Mizera’s paper. He’s found a connection between the string-theory-like CHY picture of scattering amplitudes and some unusual mathematical structures. I’m not sure what to make of it until I get a better idea of what those structures are.

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When It Rains It Amplitudes

The last few weeks have seen a rain of amplitudes papers on arXiv, including quite a few interesting ones.

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As well as a fair amount of actual rain in Copenhagen

Over the last year Nima Arkani-Hamed has been talking up four or five really interesting results, and not actually publishing any of them. This has understandably frustrated pretty much everybody. In the last week he published two of them, Cosmological Polytopes and the Wavefunction of the Universe with Paolo Benincasa and Alexander Postnikov and Scattering Amplitudes For All Masses and Spins with Tzu-Chen Huang and Yu-tin Huang. So while I’ll have to wait on the others (I’m particularly looking forward to seeing what he’s been working on with Ellis Yuan) this can at least tide me over.

Cosmological Polytopes and the Wavefunction of the Universe is Nima & co.’s attempt to get a geometrical picture for cosmological correlators, analogous to the Ampituhedron. Cosmological correlators ask questions about the overall behavior of the visible universe: how likely is one clump of matter to be some distance from another? What sorts of patterns might we see in the Cosmic Microwave Background? This is the sort of thing that can be used for “cosmological collider physics”, an idea I mention briefly here.

Paolo Benincasa was visiting Perimeter near the end of my time there, so I got a few chances to chat with him about this. One thing he mentioned, but that didn’t register fully at the time, was Postnikov’s involvement. I had expected that even if Nima and Paolo found something interesting that it wouldn’t lead to particularly deep mathematics. Unlike the N=4 super Yang-Mills theory that generates the Amplituhedron, the theories involved in these cosmological correlators aren’t particularly unique, they’re just a particular class of models cosmologists use that happen to work well with Nima’s methods. Given that, it’s really surprising that they found something mathematically interesting enough to interest Postnikov, a mathematician who was involved in the early days of the Amplituhedron’s predecessor, the Positive Grassmannian. If there’s something that mathematically worthwhile in such a seemingly arbitrary theory then perhaps some of the beauty of the Amplithedron are much more general than I had thought.

Scattering Amplitudes For All Masses and Spins is on some level a byproduct of Nima and Yu-tin’s investigations of whether string theory is unique. Still, it’s a useful byproduct. Many of the tricks we use in scattering amplitudes are at their best for theories with massless particles. Once the particles have masses our notation gets a lot messier, and we often have to rely on older methods. What Nima, Yu-tin, and Tzu-Chen have done here is to build a notation similar to what we use for massless particle, but for massive ones.

The advantage of doing this isn’t just clean-looking papers: using this notation makes it a lot easier to see what kinds of theories make sense. There are a variety of old theorems that restrict what sorts of theories you can write down: photons can’t interact directly with each other, there can only be one “gravitational force”, particles with spins greater than two shouldn’t be massless, etc. The original theorems were often fairly involved, but for massless particles there were usually nice ways to prove them in modern amplitudes notation. Yu-tin in particular has a lot of experience finding these kinds of proofs. What the new notation does is make these nice simple proofs possible for massive particles as well. For example, you can try to use the new notation to write down an interaction between a massive particle with spin greater than two and gravity, and what you find is that any expression you write breaks down: it works fine at low energies, but once you’re looking at particles with energies much higher than their mass you start predicting probabilities greater than one. This suggests that particles with higher spins shouldn’t be “fundamental”, they should be explained in terms of other particles at higher energies. The only way around this turns out to be an infinite series of particles to cancel problems from the previous ones, the sort of structure that higher vibrations have in string theory. I often don’t appreciate papers that others claim are a pleasure to read, but this one really was a pleasure to read: there’s something viscerally satisfying about seeing so many important constraints manifest so cleanly.

I’ve talked before about the difference between planar and non-planar theories. Planar theories end up being simpler, and in the case of N=4 super Yang-Mills this results in powerful symmetries that let us do much more complicated calculations. Non-planar theories are more complicated, but necessary for understanding gravity. Dual Conformal Symmetry, Integration-by-Parts Reduction, Differential Equations and the Nonplanar Sector, a new paper by Zvi Bern, Michael Enciso, Harald Ita, and Mao Zeng, works on bridging the gap between these two worlds.

Most of the paper is concerned with using some of the symmetries of N=4 super Yang-Mills in other, more realistic (but still planar) theories. The idea is that even if those symmetries don’t hold one can still use techniques that respect those symmetries, and those techniques can often be a lot cleaner than techniques that don’t. This is probably the most practically useful part of the paper, but the part I was most curious about is in the last few sections, where they discuss non-planar theories. For a while now I’ve been interested in ways to treat a non-planar theory as if it were planar, to try to leverage the powerful symmetries we have in planar N=4 super Yang-Mills elsewhere. Their trick is surprisingly simple: they just cut the diagram open! Oddly enough, they really do end up with similar symmetries using this method. I still need to read this in more detail to understand its limitations, since deep down it feels like something this simple couldn’t possibly work. Still, if anything like the symmetries of planar N=4 holds in the non-planar case there’s a lot we could do with it.

There are a bunch of other interesting recent papers that I haven’t had time to read. Some look like they might relate to weird properties of N=4 super Yang-Mills, others say interesting things about the interconnected web of theories tied together by their behavior when a particle becomes “soft”. Another presents a method for dealing with elliptic functions, one of the main obstructions to applying my hexagon function technique to more situations. And of course I shouldn’t fail to mention a paper by my colleague Carlos Cardona, applying amplitudes techniques to AdS/CFT. Overall, a lot of interesting stuff in a short span of time. I should probably get back to reading it!

Topic Conferences, Place Conferences

I spent this week at Current Themes in High Energy Physics and Cosmology, a conference at the Niels Bohr Institute.

Most conferences focus on a particular topic. Usually the broader the topic, the bigger the conference. A workshop on flux tubes is smaller than Amplitudes, which is smaller than Strings, which is smaller than the March Meeting of the American Physical Society.

“Current Themes in High Energy Physics and Cosmology” sounds like a very broad topic, but it was a small conference. The reason why is that it wasn’t a “topic conference”, it was a “place conference”.

Most conferences focus on a topic, but some are built around a place. These conferences are hosted by a particular institute year after year. Sometimes each year has a loose theme (for example, the Simons Summer Workshop this year focused on theories without supersymmetry) but sometimes no attempt is made to tie the talks together (“current themes”).

Instead of a theme, the people who go to these conferences are united by their connections to the institute. Some of them have collaborators there, or worked there in the past. Others have been coming for many years. Some just happened to be in the area.

While they may seem eclectic, “place” conferences have a valuable role: they help to keep our interests broad. In physics, there’s a natural tendency to specialize. Left alone, we end up reading papers and going to talks only when they’re directly relevant for what we’re working on. By doing this we lose track of the wider field, losing access to the insights that come from different perspectives and methods.

“Place” conferences, like seminars, help pull things in the other direction. When you’re hearing talks from “everyone connected to the Simons Center” or “everyone connected to the Niels Bohr Institute”, you’re exposed to a much broader range of topics than a conference for just your sub-field. You get a broad overview of what’s going on in the field, but unlike a big conference like Strings there are few enough people that you can actually talk to everyone.

Physicists’ attachment to places is counter-intuitive. We’re studying mathematical truths and laws of nature, surely it shouldn’t matter where we work. In practice, though, we’re still human. Out of the vast span of physics we still pick our interests based on the people around us. That’s why places, why institutes with a wide range of excellent people, are so important: they put our social instincts to work studying the universe.

More Travel

I’m visiting the Niels Bohr Institute this week, on my way back from Amplitudes.

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You might recognize the place from old conference photos.

Amplitudes itself was nice. There weren’t any surprising new developments, but a lot of little “aha” moments when one of the speakers explained something I’d heard vague rumors about. I figured I’d mention a few of the things that stood out. Be warned, this is going to be long and comparatively jargon-heavy.

The conference organizers were rather daring in scheduling Nima Arkani-Hamed for the first talk, as Nima has a tendency to arrive at the last minute and talk for twice as long as you ask him to. Miraculously, though, things worked out, if only barely: Nima arrived at the wrong campus and ran most of the way back, showing up within five minutes of the start of the conference. He also stuck to his allotted time, possibly out of courtesy to his student, Yuntao Bai, who was speaking next.

Between the two of them, Nima and Yuntao covered an interesting development, tying the Amplituhedron together with the string theory-esque picture of scattering amplitudes pioneered by Freddy Cachazo, Song He, and Ellis Ye Yuan (or CHY). There’s a simpler (and older) Amplituhedron-like object called the associahedron that can be thought of as what the Amplituhedron looks like on the surface of a string, and CHY’s setup can be thought of as a sophisticated map that takes this object and turns it into the Amplituhedron. It was nice to hear from both Nima and his student on this topic, because Nima’s talks are often high on motivation but low on detail, so it was great that Yuntao was up next to fill in the blanks.

Anastasia Volovich talked about Landau singularities, a topic I’ve mentioned before. What I hadn’t appreciated was how much they can do with them at this point. Originally, Juan Maldacena had suggested that these singularities, mathematical points that determine the behavior of amplitudes first investigated by Landau in the 60’s, might explain some of the simplicity we’ve observed in N=4 super Yang-Mills. They ended up not being enough by themselves, but what Volovich and collaborators are discovering is that with a bit of help from the Amplithedron they explain quite a lot. In particular, if they start with the Amplituhedron and do a procedure similar to Landau’s, they can find the simpler set of singularities allowed by N=4 super Yang-Mills, at least for the examples they’ve calculated. It’s still a bit unclear how this links to their previous investigations of these things in terms of cluster algebras, but it sounds like they’re making progress.

Dmitry Chicherin gave me one of those minor “aha” moments. One big useful fact about scattering amplitudes in N=4 super Yang-Mills is that they’re “dual” to different mathematical objects called Wilson loops, a fact which allows us to compare to the “POPE” approach of Basso, Sever, and Vieira. Chicherin asks the question: “What if you’re not calculating a scattering amplitude or a Wilson loop, but something halfway in between?” Interestingly, this has an answer, with the “halfway between” objects having a similar duality among themselves.

Yorgos Papathansiou talked about work I’ve been involved with. I’ll probably cover it in detail in another post, so now I’ll just mention that we’re up to six loops!

Andy Strominger talked about soft theorems. It’s always interesting seeing people who don’t traditionally work on amplitudes giving talks at Amplitudes. There’s a range of responses, from integrability people (who are basically welcomed like family) to work on fairly unrelated areas that have some “amplitudes” connection (met with yawns except from the few people interested in the connection). The response to Strominger was neither welcome nor boredom, but lively debate. He’s clearly doing something interesting, but many specialists worried he was ignorant of important no-go results in the field that could hamstring some of his bolder conjectures.

The second day focused on methods for more practical calculations, and had the overall effect of making me really want to clean up my code. Tiziano Peraro’s finite field methods in particular look like they could be quite useful. There were two competing bases of integrals on display, Von Manteuffel’s finite integrals and Rutger Boels’s uniform transcendental integrals later in the conference. Both seem to have their own virtues, and I ended up asking Rob Schabinger if it was possible to combine the two, with the result that he’s apparently now looking into it.

The more practical talks that day had a clear focus on calculations with two loops, which are becoming increasingly viable for LHC-relevant calculations. From talking to people who work on this, I get the impression that the goal of these calculations isn’t so much to find new physics as to confirm and investigate new physics found via other methods. Things are complicated enough at two loops that for the moment it isn’t feasible to describe what all the possible new particles might do at that order, and instead the goal is to understand the standard model well enough that if new physics is noticed (likely based on one-loop calculations) then the details can be pinned down by two-loop data. But this picture could conceivably change as methods improve.

Wednesday was math-focused. We had a talk by Francis Brown on his conjecture of a cosmic Galois group. This is a topic I knew a bit about already, since it’s involved in something I’ve been working on. Brown’s talk cleared up some things, but also shed light on the vagueness of the proposal. As with Yorgos’s talk, I’ll probably cover more about this in a future post, so I’ll skip the details for now.

There was also a talk by Samuel Abreu on a much more physical picture of the “symbols” we calculate with. This is something I’ve seen presented before by Ruth Britto, and it’s a setup I haven’t looked into as much as I ought to. It does seem at the moment that they’re limited to one loop, which is a definite downside. Other talks discussed elliptic integrals, the bogeyman that we still can’t deal with by our favored means but that people are at least understanding better.

The last talk on Wednesday before the hike was by David Broadhurst, who’s quite a character in his own right. Broadhurst sat in the front row and asked a question after nearly every talk, usually bringing up papers at least fifty years old, if not one hundred and fifty. At the conference dinner he was exactly the right person to read the Address to the Haggis, resurrecting a thick Scottish accent from his youth. Broadhurst’s techniques for handling high-loop elliptic integrals are quite impressively powerful, leaving me wondering if the approach can be generalized.

Thursday focused on gravity. Radu Roiban gave a better idea of where he and his collaborators are on the road to seven-loop supergravity and what the next bottlenecks are along the way. Oliver Schlotterer’s talk was another one of those “aha” moments, helping me understand a key difference between two senses in which gravity is Yang-Mills squared ( the Kawai-Lewellen-Tye relations and BCJ). In particular, the latter is much more dependent on specifics of how you write the scattering amplitude, so to the extent that you can prove something more like the former at higher loops (the original was only for trees, unlike BCJ) it’s quite valuable. Schlotterer has managed to do this at one loop, using the “Q-cut” method I’ve (briefly) mentioned before. The next day’s talk by Emil Bjerrum-Bohr focused more heavily on these Q-cuts, including a more detailed example at two loops than I’d seen that group present before.

There was also a talk by Walter Goldberger about using amplitudes methods for classical gravity, a subject I’ve looked into before. It was nice to see a more thorough presentation of those ideas, including a more honest appraisal of which amplitudes techniques are really helpful there.

There were other interesting topics, but I’m already way over my usual post length, so I’ll sign off for now. Videos from all but a few of the talks are now online, so if you’re interested you should watch them on the conference page.

Bootstrapping in the Real World

I’ll be at Amplitudes, my subfield’s big yearly conference, next week, so I don’t have a lot to talk about. That said, I wanted to give a shout-out to my collaborator and future colleague Andrew McLeod, who is a co-author (along with Øyvind Almelid, Claude Duhr, Einan Gardi, and Chris White) on a rather cool paper that went up on arXiv this week.

Andrew and I work on “bootstrapping” calculations in quantum field theory. In particular, we start with a guess for what the result will be based on a specific set of mathematical functions (in my case, “hexagon functions” involving interactions of six particles). We then narrow things down, using other calculations that by themselves only predict part of the result, until we know the right answer. The metaphor here is that we’re “pulling ourselves up by our own bootstraps”, skipping a long calculation by essentially just guessing the answer.

This method has worked pretty well…in a toy model anyway. The calculations I’ve done with it use N=4 super Yang-Mills, a simpler cousin of the theories that describe the real world. There, fewer functions can show up, so our guess is much less unwieldy than it would be otherwise.

What’s impressive about Andrew and co.’s new paper is that they apply this method, not to N=4 super Yang-Mills, but to QCD, the theory that describes quarks and gluons in the real world. This is exactly the sort of thing I’ve been hoping to see more of, these methods built into something that can help with real, useful calculations.

Currently, what they can do is still fairly limited. For the particular problem they’re looking at, the functions required ended up being relatively simple, involving interactions between at most four particles. So far, they’ve just reproduced a calculation done by other means. Going further (more “loops”) would involve interactions between more particles, as well as mixing different types of functions (different “transcendental weight”), either of which make the problem much more complicated.

That said, the simplicity of their current calculation is also a reason to be optimistic.  Their starting “guess” had just thirteen parameters, while the one Andrew and I are working on right now (in N=4 super Yang-Mills) has over a thousand. Even if things get a lot more complicated for them at the next loop, we’ve shown that “a lot more complicated” can still be quite doable.

So overall, I’m excited. It looks like there are contexts in which one really can “bootstrap” up calculations in a realistic theory, and that’s a method that could end up really useful.

You Can’t Smooth the Big Bang

As a kid, I was fascinated by cosmology. I wanted to know how the universe began, possibly disproving gods along the way, and I gobbled up anything that hinted at the answer.

At the time, I had to be content with vague slogans. As I learned more, I could match the slogans to the physics, to see what phrases like “the Big Bang” actually meant. A large part of why I went into string theory was to figure out what all those documentaries are actually about.

In the end, I didn’t end up working on cosmology due my ignorance of a few key facts while in college (mostly, who Vilenkin was). Thus, while I could match some of the old popularization stories to the science, there were a few I never really understood. In particular, there were two claims I never quite saw fleshed out: “The universe emerged from nothing via quantum tunneling” and “According to Hawking, the big bang was not a singularity, but a smooth change with no true beginning.”

As a result, I’m delighted that I’ve recently learned the physics behind these claims, in the context of a spirited take-down of both by Perimeter’s Director Neil Turok.

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My boss

Neil held a surprise string group meeting this week to discuss the paper I linked above, “No smooth beginning for spacetime” with Job Feldbrugge and Jean-Luc Lehners, as well as earlier work with Steffen Gielen. In it, he talked about problems in the two proposals I mentioned: Hawking’s suggestion that the big bang was smooth with no true beginning (really, the Hartle-Hawking no boundary proposal) and the idea that the universe emerged from nothing via quantum tunneling (really, Vilenkin’s tunneling from nothing proposal).

In popularization-speak, these two proposals sound completely different. In reality, though, they’re quite similar (and as Neil argues, they end up amounting to the same thing). I’ll steal a picture from his paper to illustrate:

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The picture on the left depicts the universe under the Hartle-Hawking proposal, with time increasing upwards on the page. As the universe gets older, it looks like the expanding (de Sitter) universe we live in. At the beginning, though, there’s a cap, one on which time ends up being treated not in the usual way (Lorentzian space) but on the same footing as the other dimensions (Euclidean space). This lets space be smooth, rather than bunching up in a big bang singularity. After treating time in this way the result is reinterpreted (via a quantum field theory trick called Wick rotation) as part of normal space-time.

What’s the connection to Vilenkin’s tunneling picture? Well, when we talk about quantum tunneling, we also end up describing it with Euclidean space. Saying that the universe tunneled from nothing and saying it has a Euclidean “cap” then end up being closely related claims.

Before Neil’s work these two proposals weren’t thought of as the same because they were thought to give different results. What Neil is arguing is that this is due to a fundamental mistake on Hartle and Hawking’s part. Specifically, Neil is arguing that the Wick rotation trick that Hartle and Hawking used doesn’t work in this context, when you’re trying to calculate small quantum corrections for gravity. In normal quantum field theory, it’s often easier to go to Euclidean space and use Wick rotation, but for quantum gravity Neil is arguing that this technique stops being rigorous. Instead, you should stay in Lorentzian space, and use a more powerful mathematical technique called Picard-Lefschetz theory.

Using this technique, Neil found that Hartle and Hawking’s nicely behaved result was mistaken, and the real result of what Hartle and Hawking were proposing looks more like Vilenkin’s tunneling proposal.

Neil then tried to see what happens when there’s some small perturbation from a perfect de Sitter universe. In general in physics if you want to trust a result it ought to be stable: small changes should stay small. Otherwise, you’re not really starting from the right point, and you should instead be looking at wherever the changes end up taking you. What Neil found was that the Hartle-Hawking and Vilenkin proposals weren’t stable. If you start with a small wiggle in your no-boundary universe you get, not the purple middle drawing with small wiggles, but the red one with wiggles that rapidly grow unstable. The implication is that the Hartle-Hawking and Vilenkin proposals aren’t just secretly the same, they also both can’t be the stable state of the universe.

Neil argues that this problem is quite general, and happens under the following conditions:

  1. A universe that begins smoothly and semi-classically (where quantum corrections are small) with no sharp boundary,
  2. with a positive cosmological constant (the de Sitter universe mentioned earlier),
  3. under which the universe expands many times, allowing the small fluctuations to grow large.

If the universe avoids one of those conditions (maybe the cosmological constant changes in the future and the universe stops expanding, for example) then you might be able to avoid Neil’s argument. But if not, you can’t have a smooth semi-classical beginning and still have a stable universe.

Now, no debate in physics ends just like that. Hartle (and collaborators) don’t disagree with Neil’s insistence on Picard-Lefschetz theory, but they argue there’s still a way to make their proposal work. Neil mentioned at the group meeting that he thinks even the new version of Hartle’s proposal doesn’t solve the problem, he’s been working out the calculation with his collaborators to make sure.

Often, one hears about an idea from science popularization and then it never gets mentioned again. The public hears about a zoo of proposals without ever knowing which ones worked out. I think child-me would appreciate hearing what happened to Hawking’s proposal for a universe with no boundary, and to Vilenkin’s proposal for a universe emerging from nothing. Adult-me certainly does. I hope you do too.

An Amplitudes Flurry

Now that we’re finally done with flurries of snow here in Canada, in the last week arXiv has been hit with a flurry of amplitudes papers.

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We’re also seeing a flurry of construction, but that’s less welcome.

Andrea Guerrieri, Yu-tin Huang, Zhizhong Li, and Congkao Wen have a paper on what are known as soft theorems. Most famously studied by Weinberg, soft theorems are proofs about what happens when a particle in an amplitude becomes “soft”, or when its momentum becomes very small. Recently, these theorems have gained renewed interest, as new amplitudes techniques have allowed researchers to go beyond Weinberg’s initial results (to “sub-leading” order) in a variety of theories.

Guerrieri, Huang, Li, and Wen’s contribution to the topic looks like it clarifies things quite a bit. Previously, most of the papers I’d seen about this had been isolated examples. This paper ties the various cases together in a very clean way, and does important work in making some older observations more rigorous.

 

Vittorio Del Duca, Claude Duhr, Robin Marzucca, and Bram Verbeek wrote about transcendental weight in something known as the multi-Regge limit. I’ve talked about transcendental weight before: loosely, it’s counting the power of pi that shows up in formulas. The multi-Regge limit concerns amplitudes with very high energies, in which we have a much better understanding of how the amplitudes should behave. I’ve used this limit before, to calculate amplitudes in N=4 super Yang-Mills.

One slogan I love to repeat is that N=4 super Yang-Mills isn’t just a toy model, it’s the most transcendental part of QCD. I’m usually fairly vague about this, because it’s not always true: while often a calculation in N=4 super Yang-Mills will give the part of the same calculation in QCD with the highest power of pi, this isn’t always the case, and it’s hard to propose a systematic principle for when it should happen. Del Duca, Duhr, Marzucca, and Verbeek’s work is a big step in that direction. While some descriptions of the multi-Regge limit obey this property, others don’t, and in looking at the ones that don’t the authors gain a better understanding of what sorts of theories only have a “maximally transcendental part”. What they find is that even when such theories aren’t restricted to N=4 super Yang-Mills, they have shared properties, like supersymmetry and conformal symmetry. Somehow these properties are tied to the transcendentality of functions in the amplitude, in a way that’s still not fully understood.

 

My colleagues at Perimeter released two papers over the last week: one, by Freddy Cachazo and Alfredo Guevara, uses amplitudes techniques to look at classical gravity, while the other, by Sebastian Mizera and Guojun Zhang, looks at one of the “pieces” inside string theory amplitudes.

I worked with Freddy and Alfredo on an early version of their result, back at the PSI Winter School. While I was off lazing about in Santa Barbara, they were hard at work trying to understand how the quantum-looking “loops” one can use to make predictions for potential energy in classical gravity are secretly classical. What they ended up finding was a trick to figure out whether a given amplitude was going to have a classical part or be purely quantum. So far, the trick works for amplitudes with one loop, and a few special cases at higher loops. It’s still not clear if it works for the general case, and there’s a lot of work still to do to understand what it means, but it definitely seems like an idea with potential. (Pun mostly not intended.)

I’ve talked before about “Z theory”, the weird thing you get when you isolate the “stringy” part of string theory amplitudes. What Sebastian and Guojun have carved out isn’t quite the same piece, but it’s related. I’m still not sure of the significance of cutting string amplitudes up in this way, I’ll have to read the paper more thoroughly (or chat with the authors) to find out.