# Pan Narrans Scientificus

As scientists, we want to describe the world as objectively as possible. We try to focus on what we can establish conclusively, to leave out excessive speculation and stick to cold, hard facts.

Then we have to write application letters.

Stick to the raw, un-embellished facts, and an application letter would just be a list: these papers in these journals, these talks and awards. Though we may sometimes wish applications worked that way, we don’t live in that kind of world. To apply for a job or a grant, we can’t just stick to the most easily measured facts. We have to tell a story.

The author Terry Pratchett called humans Pan Narrans, the Storytelling Ape. Stories aren’t just for fun, they’re how we see the world, how we organize our perceptions and actions. Without a story, the world doesn’t make sense. And that applies even to scientists.

Applications work best when they tell a story: how did you get here, and where are you going? Scientific papers, similarly, require some sort of narrative: what did you do, and why did you do it? When teaching or writing about science, we almost never just present the facts. We try to fit it into a story, one that presents the facts but also makes sense, in that deliciously human way. A story, more than mere facts, lets us project to the future, anticipating what you’ll do with that grant money or how others will take your research in new directions.

It’s important to remember, though, that stories aren’t actually facts. You can’t get too attached to one story, you have to be willing to shift as new facts come in. Those facts can be scientific measurements, but they can also be steps in your career. You aren’t going to tell the same story when applying to grad school as when you’re trying for tenure, and that’s not just because you’ll have more to tell. The facts of your life will be organized in new ways, rearranging in importance as the story shifts.

Keep your stories in mind as you write or do science. Think about your narrative, the story you’re using to understand the world. Think about what it predicts, how the next step in the story should go. And be ready to start a new story when you need to.

# My Other Brain (And My Other Other Brain)

What does a theoretical physicist do all day? We sit and think.

Most of us can’t do all that thinking in our heads, though. Maybe Steven Hawking could, but the rest of us need to visualize what we’re thinking. Our memories, too, are all-too finite, prone to forget what we’re doing midway through a calculation.

So rather than just use our imagination and memory, we use another imagination, another memory: a piece of paper. Writing is the simplest “other brain” we have access to, but even by itself it’s a big improvement, adding weeks of memory and the ability to “see” long calculations at work.

But even augmented by writing, our brains are limited. We can only calculate so fast. What’s more, we get bored: doing the same thing mechanically over and over is not something our brains like to do.

Luckily, in the modern era we have access to other brains: computers.

As I write, the “other brain” sitting on my desk works out a long calculation. Using programs like Mathematica or Maple, or more serious programming languages, I can tell my “other brain” to do something and it will do it, quickly and without getting bored.

My “other brain” is limited too. It has only so much memory, only so much speed, it can only do so many calculations at once. While it’s thinking, though, I can find yet another brain to think at the same time. Sometimes that’s just my desktop, sitting back in my office in Denmark. Sometimes I have access to clusters, blobs of synchronized brains to do my bidding.

While I’m writing this, my “brains” are doing five different calculations (not counting any my “real brain” might be doing). I’m sitting and thinking, as a theoretical physicist should.

# Amplitudes in the LHC Era at GGI

I’m at the Galileo Galilei Institute in Florence this week, for a program on Amplitudes in the LHC Era.

I didn’t notice this ceiling decoration last time I was here. These guys really love their Galileo stuff.

I’ll be here for three weeks of the full six-week program, hopefully plenty of time for some solid collaboration. This week was the “conference part”, with a flurry of talks over three days.

I missed the first day, which focused on the “actually useful” side of scattering amplitudes, practical techniques that can be applied to real Standard Model calculations. Luckily the slides are online, and at least some of the speakers are still around to answer questions. I’m particularly curious about Daniel Hulme’s talk, about an approximation strategy I hadn’t heard of before.

The topics of the next two days were more familiar, but the talks still gave me a better appreciation for the big picture behind them. From Johannes Henn’s thoughts about isolating a “conformal part” of general scattering amplitudes to Enrico Herrmann’s roadmap for finding an amplituhedron for supergravity, people seem to be aiming for bigger goals than just the next technical hurdle. It will be nice to settle in over the next couple weeks and get a feeling for what folks are working on next.

# A Micrographia of Beastly Feynman Diagrams

Earlier this year, I had a paper about the weird multi-dimensional curves you get when you try to compute trickier and trickier Feynman diagrams. These curves were “Calabi-Yau”, a type of curve string theorists have studied as a way to curl up extra dimensions to preserve something called supersymmetry. At the time, string theorists asked me why Calabi-Yau curves showed up in these Feynman diagrams. Do they also have something to do with supersymmetry?

I still don’t know the general answer. I don’t know if all Feynman diagrams have Calabi-Yau curves hidden in them, or if only some do. But for a specific class of diagrams, I now know the reason. In this week’s paper, with Jacob Bourjaily, Andrew McLeod, and Matthias Wilhelm, we prove it.

We just needed to look at some more exotic beasts to figure it out.

Like this guy!

Meet the tardigrade. In biology, they’re incredibly tenacious microscopic animals, able to withstand the most extreme of temperatures and the radiation of outer space. In physics, we’re using their name for a class of Feynman diagrams.

A clear resemblance!

There is a long history of physicists using whimsical animal names for Feynman diagrams, from the penguin to the seagull (no relation). We chose to stick with microscopic organisms: in addition to the tardigrades, we have paramecia and amoebas, even a rogue coccolithophore.

The diagrams we look at have one thing in common, which is key to our proof: the number of lines on the inside of the diagram (“propagators”, which represent “virtual particles”) is related to the number of “loops” in the diagram, as well as the dimension. When these three numbers are related in the right way, it becomes relatively simple to show that any curves we find when computing the Feynman diagram have to be Calabi-Yau.

This includes the most well-known case of Calabi-Yaus showing up in Feynman diagrams, in so-called “banana” or “sunrise” graphs. It’s closely related to some of the cases examined by mathematicians, and our argument ended up pretty close to one made back in 2009 by the mathematician Francis Brown for a different class of diagrams. Oddly enough, neither argument works for the “traintrack” diagrams from our last paper. The tardigrades, paramecia, and amoebas are “more beastly” than those traintracks: their Calabi-Yau curves have more dimensions. In fact, we can show they have the most dimensions possible at each loop, provided all of our particles are massless. In some sense, tardigrades are “as beastly as you can get”.

We still don’t know whether all Feynman diagrams have Calabi-Yau curves, or just these. We’re not even sure how much it matters: it could be that the Calabi-Yau property is a red herring here, noticed because it’s interesting to string theorists but not so informative for us. We don’t understand Calabi-Yaus all that well yet ourselves, so we’ve been looking around at textbooks to try to figure out what people know. One of those textbooks was our inspiration for the “bestiary” in our title, an author whose whimsy we heartily approve of.

Like the classical bestiary, we hope that ours conveys a wholesome moral. There are much stranger beasts in the world of Feynman diagrams than anyone suspected.

# Don’t Marry Your Arbitrary

This fall, I’m TAing a course on General Relativity. I haven’t taught in a while, so it’s been a good opportunity to reconnect with how students think.

This week, one problem left several students confused. The problem involved Christoffel symbols, the bane of many a physics grad student, but the trick that they had to use was in the end quite simple. It’s an example of a broader trick, a way of thinking about problems that comes up all across physics.

To see a simplified version of the problem, imagine you start with this sum:

$g(j)=\Sigma_{i=0}^n ( f(i,j)-f(j,i) )$

Now, imagine you want to sum the function $g(j)$ over $j$. You can write:

$\Sigma_{j=0}^n g(j) = \Sigma_{j=0}^n \Sigma_{i=0}^n ( f(i,j)-f(j,i) )$

Let’s break this up into two terms, for later convenience:

$\Sigma_{j=0}^n g(j) = \Sigma_{j=0}^n \Sigma_{i=0}^n f(i,j) - \Sigma_{j=0}^n \Sigma_{i=0}^n f(j,i)$

Without telling you anything about $f(i,j)$, what do you know about this sum?

Well, one thing you know is that $i$ and $j$ are arbitrary.

$i$ and $j$ are letters you happened to use. You could have used different letters, $x$ and $y$, or $\alpha$ and $\beta$. You could even use different letters in each term, if you wanted to. You could even just pick one term, and swap $i$ and $j$.

$\Sigma_{j=0}^n g(j) = \Sigma_{j=0}^n \Sigma_{i=0}^n f(i,j) - \Sigma_{i=0}^n \Sigma_{j=0}^n f(i,j) = 0$

And now, without knowing anything about $f(i,j)$, you know that $\Sigma_{j=0}^n g(j)$ is zero.

In physics, it’s extremely important to keep track of what could be really physical, and what is merely your arbitrary choice. In general relativity, your choice of polar versus spherical coordinates shouldn’t affect your calculation. In quantum field theory, your choice of gauge shouldn’t matter, and neither should your scheme for regularizing divergences.

Ideally, you’d do your calculation without making any of those arbitrary choices: no coordinates, no choice of gauge, no regularization scheme. In practice, sometimes you can do this, sometimes you can’t. When you can’t, you need to keep that arbitrariness in the back of your mind, and not get stuck assuming your choice was the only one. If you’re careful with arbitrariness, it can be one of the most powerful tools in physics. If you’re not, you can stare at a mess of Christoffel symbols for hours, and nobody wants that.

# Conferences Are Work! Who Knew?

I’ve been traveling for over a month now, from conference to conference, with a bit of vacation thrown in at the end.

(As such, I haven’t had time to read up on the recent announcement of the detection of neutrinos and high-energy photons from a blazar, Matt Strassler has a nice piece on it.)

One thing I didn’t expect was how exhausting going to three conferences in a row would be. I didn’t give any talks this time around, so I thought I was skipping the “work” part. But sitting in a room for talk after talk, listening and taking notes, turns out to still be work! There’s effort involved in paying attention, especially in a scientific talk where the details matter. You assess the talks in your head, turning concepts around and thinking about what you might do with them. It’s the kind of thing you don’t notice for a seminar or two, but at a conference, after a while, it really builds up. After three, let’s just say I’ve really needed this vacation. I’ll be back at work next week, and maybe I’ll have a longer blog post for you folks. Until then, I ought to get some rest!

# Amplitudes 2018

This week, I’m at Amplitudes, my field’s big yearly conference. The conference is at SLAC National Accelerator Laboratory this year, a familiar and lovely place.

Welcome to the Guest House California

It’s been a packed conference, with a lot of interesting talks. Recording and slides of most of them should be up at this point, for those following at home. I’ll comment on a few that caught my attention, I might do a more in-depth post later.

The first morning was dedicated to gravitational waves. At the QCD Meets Gravity conference last December I noted that amplitudes folks were very eager to do something relevant to LIGO, but that it was still a bit unclear how we could contribute (aside from Pierpaolo Mastrolia, who had already figured it out). The following six months appear to have cleared things up considerably, and Clifford Cheung and Donal O’Connel’s talks laid out quite concrete directions for this kind of research.

I’d seen Erik Panzer talk about the Hepp bound two weeks ago at Les Houches, but that was for a much more mathematically-inclined audience. It’s been interesting seeing people here start to see the implications: a simple method to classify and estimate (within 1%!) Feynman integrals could be a real game-changer.

Brenda Penante’s talk made me rethink a slogan I like to quote, that N=4 super Yang-Mills is the “most transcendental” part of QCD. While this is true in some cases, in many ways it’s actually least true for amplitudes, with quite a few counterexamples. For other quantities (like the form factors that were the subject of her talk) it’s true more often, and it’s still unclear when we should expect it to hold, or why.

Nima Arkani-Hamed has a reputation for talks that end up much longer than scheduled. Lately, it seems to be due to the sheer number of projects he’s working on. He had to rush at the end of his talk, which would have been about cosmological polytopes. I’ll have to ask his collaborator Paolo Benincasa for an update when I get back to Copenhagen.

Tuesday afternoon was a series of talks on the “NNLO frontier”, two-loop calculations that form the state of the art for realistic collider physics predictions. These talks brought home to me that the LHC really does need two-loop precision, and that the methods to get it are still pretty cumbersome. For those of us off in the airy land of six-loop N=4 super Yang-Mills, this is the challenge: can we make what these people do simpler?

Wednesday cleared up a few things for me, from what kinds of things you can write down in “fishnet theory” to how broad Ashoke Sen’s soft theorem is, to how fast John Joseph Carrasco could show his villanelle slide. It also gave me a clearer idea of just what simplifications are available for pushing to higher loops in supergravity.

Wednesday was also the poster session. It keeps being amazing how fast the field is growing, the sheer number of new faces was quite inspiring. One of those new faces pointed me to a paper I had missed, suggesting that elliptic integrals could end up trickier than most of us had thought.

Thursday featured two talks by people who work on the Conformal Bootstrap, one of our subfield’s closest relatives. (We’re both “bootstrappers” in some sense.) The talks were interesting, but there wasn’t a lot of engagement from the audience, so if the intent was to make a bridge between the subfields I’m not sure it panned out. Overall, I think we’re mostly just united by how we feel about Simon Caron-Huot, who David Simmons-Duffin described as “awesome and mysterious”. We also had an update on attempts to extend the Pentagon OPE to ABJM, a three-dimensional analogue of N=4 super Yang-Mills.

I’m looking forward to Friday’s talks, promising elliptic functions among other interesting problems.