Gauge-fixing local H symmetry in supergravities

TL;DR

This paper investigates gauge-fixing procedures for local H symmetries in supergravities, analyzing how different gauge choices affect the manifest symmetries and their implications for S-matrix equivalences.

Contribution

It provides explicit gauge-fixing methods in various gauges for supergravities and discusses the impact on symmetry realization and S-matrix equivalence.

Findings

Symmetric gauge preserves global H-invariance and G-symmetry on shell in 4D supergravity.

Iwasawa gauges break manifest H and G symmetries, affecting S-matrix calculations.

Gauge choices influence the manifest symmetries and the relation between different supergravity formulations.

Abstract

We discuss known maximal D-dimensional supergravities of two types: type I with G/H coset spaces and type II derived by compactification from higher dimensions without dualization, these have less manifest symmetries. In 4D and 6D in type I models we perform explicit gauge-fixing of local H symmetries in unitary gauges: symmetric, Iwasawa, and partial Iwasawa. In 4D supergravity I in symmetric gauge global H-invariance and nonlinearly realized G-symmetry are valid on shell, classically. The global H-symmetry and G-symmetry in Iwasawa-type gauges in type I and type II supergravities are not manifest, if at all present. This fact raises the issue of the gauge equivalence of the S-matrix of various gauge-fixed D-dimensional supergravities and its relation to the ones computable using superamplitude methods.