Electric/magnetic duality for chiral gauge theories with anomaly cancellation

TL;DR

This paper develops a covariant formulation of 4D gauge theories with anomaly cancellation, extending previous work to include anomalous interactions and diverse duality frames relevant in string theory and supergravity.

Contribution

It generalizes the symplectically covariant formulation to include anomalous gauge theories by relaxing constraints on the embedding tensor, accommodating various duality frames and anomaly structures.

Findings

Formulation is covariant under electric/magnetic duality.

Includes theories with (pseudo-)anomalous gauge interactions.

Can describe duality frames in string compactifications with fluxes.

Abstract

We show that 4D gauge theories with Green-Schwarz anomaly cancellation and possible generalized Chern-Simons terms admit a formulation that is manifestly covariant with respect to electric/magnetic duality transformations. This generalizes previous work on the symplectically covariant formulation of anomaly-free gauge theories as they typically occur in extended supergravity, and now also includes general theories with (pseudo-)anomalous gauge interactions as they may occur in global or local N=1 supersymmetry. This generalization is achieved by relaxing the linear constraint on the embedding tensor so as to allow for a symmetric 3-tensor related to electric and/or magnetic quantum anomalies in these theories. Apart from electric and magnetic gauge fields, the resulting Lagrangians also feature two-form fields and can accommodate various unusual duality frames as they often appear, e.g., in string compactifications with background fluxes.