Form factors of $\mathscr{N}=4$ self-dual Yang-Mills from the chiral algebra bootstrap

TL;DR

This paper applies the chiral algebra bootstrap to self-dual 4d N=4 super Yang-Mills, deriving all-loop collinear splitting functions and computing new form factors, advancing understanding of self-dual gauge theories.

Contribution

It introduces a novel bootstrap approach to self-dual gauge theories, deriving all-loop splitting functions and form factors, including proofs of key properties like absence of double-poles.

Findings

Derived all-loop holomorphic collinear splitting functions for SDSYM.

Provided a simple proof that there are no double-poles in loop-level OPEs.

Computed several form factors, including novel two-loop results involving anti-self-dual fields.

Abstract

The chiral algebra bootstrap (CAB) is a novel bootstrap program for form factors in quantum-integrable self-dual gauge theories, some of which in turn are helicity amplitudes in the corresponding gauge theories. The singularities that recursively generate a given (loop-level) form factor are holomorphic collinear splitting functions, equivalently celestial chiral algebra OPEs, of the self-dual theory. In this note, we apply the chiral algebra bootstrap to the simple example of self-dual 4d $\mathscr{N}=4$ super Yang-Mills (SDSYM). We use a combination of twistor space input, Koszul duality, supersymmetry, and associativity to obtain the all-loop holomorphic collinear splitting functions for SDSYM. We also use associativity to provide a simple proof of the conjecture that there are no double-poles in the loop-level OPEs for this theory. We conclude by computing several form factors, including both a reproduction of several known results and novel form factors up to two loops involving insertions of powers of the anti-self-dual field strength. These form factors compute a supersymmetric version of Higgs amplitudes in the self-dual sector. Detailed sample computations are provided to familiarize the reader with the CAB method.