Non-abelian 4-d black holes, wrapped 5-branes, and their dual descriptions

TL;DR

This paper explores non-abelian black hole solutions and wrapped 5-branes, revealing their thermodynamic properties, phase transitions, and potential implications for string theory and cosmology.

Contribution

It introduces new non-extremal and extremal solutions with regular horizons, linking black hole thermodynamics to gauge theory phenomena and string theory constructs.

Findings

Black hole entropy decreases at high temperatures, indicating thermodynamic instability.

Chiral symmetry restoration occurs at high energy densities in these solutions.

Explicit sigma models with linear dilaton are constructed in certain limits.

Abstract

We study extremal and non-extremal generalizations of the regular non-abelian monopole solution of hep-th/9707176, interpreted in hep-th/0007018 as 5-branes wrapped on a shrinking S^2. Naively, the low energy dynamics is pure N=1 supersymmetric Yang-Mills. However, our results suggest that the scale of confinement and chiral symmetry breaking in the Yang-Mills theory actually coincides with the Hagedorn temperature of the little string theory. We find solutions with regular horizons and arbitrarily high Hawking temperature. Chiral symmetry is restored at high energy density, corresponding to large black holes. But the entropy of the black hole solutions decreases as one proceeds to higher temperatures, indicating that there is a thermodynamic instability and that the canonical ensemble is ill-defined. For certain limits of the black hole solutions, we exhibit explicit non-linear sigma models involving a linear dilaton. In other limits we find extremal non-BPS solutions which may have some relevance to string cosmology.