Matter Couplings and Equivalence Principles for Soft Scalars

TL;DR

This paper investigates matter couplings in scalar effective field theories with enhanced soft limits, revealing universal coupling principles and soft theorems that resemble gauge and gravity theories, and constructing a new galileon-vector theory.

Contribution

It demonstrates that matter fields couple universally to DBI and galileon scalars via specific vertices, establishing scalar analogues of the equivalence principle and soft theorems.

Findings

Universal matter coupling via quartic vertices

Scalar double soft theorems analogous to Weinberg's gravitational theorem

Construction of a new galileon-vector effective field theory

Abstract

Scalar effective field theories with enhanced soft limits behave in many ways like gauge theories and gravity. In particular, symmetries fix the structure of interactions and the tree-level S-matrix in both types of theories. We explore how this analogy persists in the presence of matter by considering theories with additional fields coupled to the Dirac-Born-Infeld (DBI) scalar or the special galileon in a way that is consistent with their symmetries. Using purely on-shell arguments, we show that these theories obey analogues of the S-matrix equivalence principle whereby all matter fields must couple to the DBI scalar or the special galileon through a particular quartic vertex with a universal coupling. These equivalence principles imply the universality of the leading double soft theorems in these theories, which are scalar analogues of Weinberg's gravitational soft theorem, and can be used to rule out interactions with massless higher-spin fields when combined with analogues of the generalized Weinberg-Witten theorem. We verify in several examples that amplitudes with external matter fields nontrivially exhibit enhanced single soft limits and we show that such amplitudes can be constructed using soft recursion relations when they have sufficiently many external DBI or special galileon legs, including amplitudes with massive higher-spin fields. As part of our analysis we construct a recently conjectured special galileon-vector effective field theory.