Gauging hidden symmetries in two dimensions

TL;DR

This paper develops a systematic framework for constructing gauged supergravity theories in two dimensions, revealing hidden symmetries and classifying possible gaugings via an embedding tensor within an infinite-dimensional symmetry algebra.

Contribution

It introduces a group-theoretic approach to classify and construct gauged supergravity theories in two dimensions using an embedding tensor in the affine E_9 algebra.

Findings

Identifies the role of hidden symmetries in gauged supergravity.

Provides a systematic classification of gaugings via the embedding tensor.

Explores examples with higher-dimensional origins and their algebraic structures.

Abstract

We initiate the systematic construction of gauged matter-coupled supergravity theories in two dimensions. Subgroups of the affine global symmetry group of toroidally compactified supergravity can be gauged by coupling vector fields with minimal couplings and a particular topological term. The gauge groups typically include hidden symmetries that are not among the target-space isometries of the ungauged theory. The possible gaugings are described group-theoretically in terms of a constant embedding tensor subject to a number of constraints which parametrizes the different theories and entirely encodes the gauged Lagrangian. The prime example is the bosonic sector of the maximally supersymmetric theory whose ungauged version admits an affine E_9 global symmetry algebra. The various parameters (related to higher-dimensional p-form fluxes, geometric and non-geometric fluxes, etc.) which characterize the possible gaugings, combine into an embedding tensor transforming in the basic representation of E_9. This yields an infinite-dimensional class of maximally supersymmetric theories in two dimensions. We work out and discuss several examples of higher-dimensional origin which can be systematically analyzed using the different gradings of E_9.