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

We study extremal and non-extremal generalizations of the regular non-abelianmonopole solution of hep-th/9707176, interpreted in hep-th/0007018 as 5-braneswrapped on a shrinking S^2. Naively, the low energy dynamics is pure N=1supersymmetric Yang-Mills. However, our results suggest that the scale ofconfinement and chiral symmetry breaking in the Yang-Mills theory actuallycoincides with the Hagedorn temperature of the little string theory. We findsolutions with regular horizons and arbitrarily high Hawking temperature.Chiral symmetry is restored at high energy density, corresponding to largeblack holes. But the entropy of the black hole solutions decreases as oneproceeds to higher temperatures, indicating that there is a thermodynamicinstability and that the canonical ensemble is ill-defined. For certain limitsof the black hole solutions, we exhibit explicit non-linear sigma modelsinvolving a linear dilaton. In other limits we find extremal non-BPS solutionswhich may have some relevance to string cosmology.Comment: 53 pages, 21 figures, latex. v2: slightly improved figure