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.


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.

6 thoughts on “An Amplitudes Flurry

    1. 4gravitonsandagradstudent Post author

      So, as usual it’s important to distinguish low-energy supersymmetry (and supergravity) from whether those properties hold at high energies. I’m not familiar with the experiments you’re referring to (if you could provide a link to a relevant article that would be helpful), but my guess is that the most that sort of thing could do would be to put limits on gravitino masses. That said, I may be misunderstanding the context of your question.

      Liked by 1 person

      1. giuliohome

        Thank you very much for your kind answer! The starting point “There are theoretical models predicting that spin and gravity should couple; that is, depending on its spin a particle should behave in different ways in a gravitational field,” of the question I posted is from a quote of the interview at url: Recently there has a new experiment reported by Italian media (if I’m not wrong this is maybe a related arxiv Thank you in advance for any further comments from you 🙂


        1. 4gravitonsandagradstudent Post author

          Ah, I see what you’re asking about. The impression I have is that these are distinct issues. I don’t usually hear people refer to supergravity theories as violating the equivalence principle, so I think the answer you got on stackexchange was misunderstanding part of your question. But I may be confusing myself on this.

          Liked by 1 person

            1. 4gravitonsandagradstudent Post author

              It looks like you heard back from the guy on stackexchange, but I thought you might be interested in this paper. It’s a constraint on graviphotons and graviscalars, not gravitinos, so it’s not the same thing you were asking about, and I haven’t found more recent work by the authors on the topic so I’m not sure if it’s obsolete, but it does indicate that those sorts of experiments can place some constraints on the masses of supergravity fields. The constraints (at least in that paper) look weaker than the constraints we have at this point from the LHC though.

              Liked by 1 person


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