Extensions of Theories from Soft Limits

TL;DR

This paper explores how certain field theories with vanishing soft limits can be extended by larger theories, revealing new interactions and providing explicit CHY representations for their complete tree-level S-matrices.

Contribution

It introduces extended theories for NLSM, Galileon, and Born-Infeld models, with explicit CHY formulas and a novel recursion relation for the extended NLSM S-matrix.

Findings

Extended theories include additional fields and interactions.

CHY representations for the full tree-level S-matrices are proposed.

A compact BCFW-like recursion relation is derived for the extended NLSM.

Abstract

We study a variety of field theories with vanishing single soft limits. In all cases, the structure of the soft limit is controlled by a larger theory, which provides an extension of the original one by adding more fields and interactions. Our main example is the $U(N)$ non-linear sigma model in its CHY representation. Its extension is a theory in which the NLSM Goldstone bosons interact with a cubic biadjoint scalar. Other theories we study and extend are the special Galileon and Born-Infeld theory, including its maximally supersymmetric version in four dimensions, the DBI-Volkov-Akulov theory. In all the cases, we propose the CHY representation of the complete tree-level S-matrix of the extended theories. In fact, CHY formulas are the key technique for studying the single soft limit behavior of the original theories. As a byproduct, we show that the tree-level S-matrix of the extended NLSM theory can be constructed using a very compact BCFW-like recursion relation, where physical poles are at most linear in the deformation parameter.