Charging Symmetries and Linearizing Potentials for Gravity Models with Symplectic Symmetry

TL;DR

This paper investigates symmetries in four-dimensional gravity models with multiple vector fields, focusing on their reduction to three dimensions, and introduces new variables and invariants to better understand their structure.

Contribution

The study explicitly formulates non-gauge symmetries using Ernst potentials, constructs new linearly transforming matrix variables, and identifies a key invariant of the symmetry subgroup.

Findings

Explicit form of non-gauge symmetries derived

New matrix variables linearly transforming under symmetries introduced

A general invariant of the symmetry subgroup established

Abstract

In this paper we continue to study a class of four-dimensional gravity models with n Abelian vector fields and Sp(2n)/U(n) coset of scalar fields. This class contains General Relativity (n=0) and Einstein-Maxwell dilaton-axion theory (n=1), which arizes in the low-energy limit of heterotic string theory. We perform reduction of the model with arbitrary $n$ to three dimensions and study the subgroup of non-gauge symmetries of the resulting theory. First, we find an explicit form these symmetries using Ernst matrix potential formulation. Second, we construct new matrix variable which linearly transforms under the action of the non-gauge transformations. Finally, we establish one general invariant of the non-gauge symmetry subgroup, which allow us to clarify this subgroup structure.