The Infrared Structure of Exceptional Scalar Theories

TL;DR

This paper systematically studies exceptional scalar theories with enhanced soft limits, revealing their underlying symmetries, deriving new recursion relations, and constructing an extended theory with a rich particle spectrum.

Contribution

It extends the soft theorem approach to a broader class of exceptional scalar theories and constructs a new Lagrangian for the extended special Galileon theory.

Findings

Identified Feynman vertices of the extended special Galileon theory.

Derived subleading single soft theorems for these theories.

Presented a Lagrangian for the extended special Galileon theory with diverse particle content.

Abstract

Exceptional theories are a group of one-parameter scalar field theories with (enhanced) vanishing soft limits in the S-matrix elements. They include the nonlinear sigma model (NLSM), Dirac-Born-Infeld scalars and the special Galileon theory. The soft behavior results from the shift symmetry underlying these theories, which leads to Ward identities generating subleading single soft theorems as well as novel Berends-Giele recursion relations. Such an approach was first applied to NLSM in 1709.08639 and 1804.08629, and here we use it to systematically study other exceptional scalar field theories. In particular, using the subleading single soft theorem for the special Galileon we identify the Feynman vertices of the corresponding extended theory, which was first discovered using the Cachazo-He-Yuan representation of scattering amplitudes. Furthermore, we present a Lagrangian for the extended theory of the special Galileon, which has a rich particle content involving biadjoint scalars, Nambu-Goldstone bosons and Galileons, as well as additional flavor structure.