Dynamics and BPS states of AdS5 supergravity with a Gauss-Bonnet term

TL;DR

This paper explores the complex dynamics of five-dimensional supergravity with a Gauss-Bonnet term, revealing diverse phase space sectors, explicit AdS solutions, BPS states, and the impact of matter fields on charge algebra.

Contribution

It introduces a detailed analysis of supergravity with a Gauss-Bonnet term, identifying regular and irregular sectors, and constructs explicit solutions including BPS states with central charge extensions.

Findings

Existence of regular, locally AdS solutions with nontrivial gauge fields.

Identification of BPS states and their charge algebra extensions.

Discovery of irregular sectors in phase space, especially in the N=4 case.

Abstract

Some dynamical aspects of five-dimensional supergravity as a Chern-Simons theory for the SU(2,2|N) group, are analyzed. The gravitational sector is described by the Einstein-Hilbert action with negative cosmological constant and a Gauss-Bonnet term with a fixed coupling. The interaction between matter and gravity is characterized by intricate couplings which give rise to dynamical features not present in standard theories. Depending on the location in phase space, the dynamics can possess different number of propagating degrees of freedom, including purely topological sectors. This inhomogeneity of phase space requires special care in the analysis. Background solutions in the canonical sectors, which have regular dynamics with maximal number of degrees of freedom, are shown to exist. Within this class, explicit solutions given by locally AdS spacetimes with nontrivial gauge fields are constructed, and BPS states are identified. It is shown that the charge algebra acquires a central extension due to the presence of the matter fields. The Bogomol'nyi bound for these charges is discussed. Special attention is devoted to the N=4 case since then the gauge group has a U(1) central charge and the phase space possesses additional irregular sectors.