SL(4,R) generating symmetry in five-dimensional gravity coupled to dilaton and three-form

TL;DR

This paper formulates an explicit SL(4,R)/SO(2,2) sigma-model for five-dimensional gravity coupled to a dilaton and three-form, revealing symmetries that generate new solutions like rotating strings and branes.

Contribution

It introduces a new matrix representation of the SL(4,R) symmetry in 5D gravity with matter fields, enabling the construction of novel solutions from known ones.

Findings

Derived explicit sigma-model formulation for 5D gravity with matter.

Identified SL(4,R) symmetry transformations linking various solutions.

Constructed new rotating string and brane solutions with NUT parameters.

Abstract

We give an explicit formulation of the three-dimensional $SL(4,R)/SO(2,2) \sigma$-model representing the five-dimensional Einstein gravity coupled to the dilaton and the three-form field for spacetimes with two commuting Killing vector fields. New matrix representation is obtained which is similar to one found earlier in the four-dimensional Einstein-Maxwell-Dilaton-Axion (EMDA) theory. The SL(4,R) symmetry joins a variety of 5D solutions of different physical types including strings, 0-branes, KK monopoles etc. interpreting them as duals to the four-dimensional Kerr metric translated along the fifth coordinate. The symmetry transformations are used to construct new rotating strings and composite 0-1-branes endowed with a NUT parameter.