Soft theorems from anomalous symmetries

TL;DR

This work analyzes soft theorems for anomalous symmetries in quantum field theories, focusing on dilaton-driven conformal anomalies and U(1) duality anomalies in N=4 supergravity. It derives how single-soft limits are modified by anomaly variations via δΓ while showing double-soft limits remain governed by coset and current algebra; it then applies these insights to constrain R^4-type counterterms using string-theory α' expansions and demonstrates a duality-preserving non-linear completion consistent up to seven points. A key result is that, despite anomalies, soft theorems impose concrete relations among amplitudes across multiplicities and dimensions, and that universal transcendental coefficients in α' expansions underpin the structure of higher-loop divergences. Overall, the paper clarifies how anomalous symmetries shape effective actions and UV behavior, while highlighting that duality and SUSY alone do not fully explain finiteness in N=4 supergravity, motivating further bootstrap approaches.

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.