Soft theorems from anomalous symmetries

TL;DR

This paper explores how anomalous symmetries impose soft theorems on effective field theories, verifying these theorems in various contexts including string theory and supergravity, and constructing duality-invariant R^4 completions.

Contribution

It demonstrates the validity of soft theorems for anomalous symmetries in effective theories and constructs duality-invariant R^4 completions up to seven points.

Findings

Soft theorems hold for dilaton and supergravity effective actions.

Constructed duality-invariant R^4 completions up to seven points.

Verified soft theorems using string theory amplitude expansions.

Abstract

We discuss constraints imposed by soft limits for effective field theories arising from symmetry breaking. In particular, we consider those associated with anomalous conformal symmetry as well as duality symmetries in supergravity. We verify these soft theorems for the dilaton effective action relevant for the a-theorem, as well as the one-loop effective action for N=4 supergravity. Using the universality of leading transcendental coefficients in the alpha' expansion of string theory amplitudes, we study the matrix elements of operator R^4 with half maximal supersymmetry. We construct the non-linear completion of R^4 that satisfies both single and double soft theorems up to seven points. This supports the existence of duality invariant completion of R^4.