AdS_5 solutions in Einstein--Yang-Mills--Chern-Simons theory

TL;DR

This paper explores static, spherically symmetric solutions in Einstein-Yang-Mills-Chern-Simons theory with negative cosmological constant, revealing new regular and black hole solutions with implications for dual field theories.

Contribution

It introduces novel solutions in Einstein-Yang-Mills-Chern-Simons theory, including regular and black hole configurations, highlighting the role of the Chern-Simons term in non-Abelian gauge fields.

Findings

Existence of regular and black hole solutions with nontrivial gauge fields.

Divergent mass solutions imply non-zero stress tensor trace in dual theory.

Finite mass solutions depend on the Chern-Simons coupling.

Abstract

We investigate static, spherically symmetric solutions of an Einstein-Yang-Mills-Chern-Simons system with negative cosmological constant, for an SO(6) gauge group. For a particular value of the Chern-Simons coefficient, this model can be viewed as a truncation of the five-dimensional maximal gauged supergravity and we expect that the basic properties of the solutions in the full model to persist in this truncation. Both globally regular, particle-like solutions and black holes are considered. In contrast with the Abelian case, the contribution of the Chern-Simons term is nontrivial already in the static, spherically symmetric limit. We find two types of solutions: the generic configurations whose magnetic gauge field does not vanish fast enough at infinity (although the spacetime is asymptotically AdS), whose mass function is divergent, and the special configurations, whose existence depends on the Chern--Simons term, which are endowed with finite mass. In the case of the generic configurations, we argue that the divergent mass implies a nonvanishing trace for the stress tensor of the dual d=4 theory.