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

Steven S. Gubser, Arkady A. Tseytlin, Mikhail S. Volkov

TL;DR

This work examines holographic descriptions of confinement and chiral symmetry breaking in ${ m N}=1$ super-Yang–Mills via wrapped 5-branes on a shrinking ${f S}^2$, connecting four-dimensional gauged ${ m N}=4$ supergravity solutions to ten-dimensional backgrounds of type IIB string theory. The authors construct and analyze extremal (BPS and non-BPS) and non-extremal black-hole configurations, identifying a two-branch structure (abelian and non-abelian) and deriving the Hawking-temperature behavior of the horizons. A key finding is that the confinement/chiral-breaking scale coincides with the Hagedorn temperature $T_c$ of the little string theory, while the canonical ensemble is thermodynamically unstable due to negative specific heat, implying subtle UV/massive-mode couplings and potential Gregory–Laflamme-type instabilities. In certain limits they obtain explicit non-linear sigma models with a linear dilaton and a simple Abelian solution with a NS-NS coset sigma-model counterpart, suggesting connections to exact world-sheet CFTs. Overall, the work sheds light on how UV completions (little string theory) influence low-energy gauge dynamics in holographic confining backgrounds and highlights the nuanced thermodynamics of wrapped 5-brane constructions.

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.

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

TL;DR

This work examines holographic descriptions of confinement and chiral symmetry breaking in super-Yang–Mills via wrapped 5-branes on a shrinking , connecting four-dimensional gauged supergravity solutions to ten-dimensional backgrounds of type IIB string theory. The authors construct and analyze extremal (BPS and non-BPS) and non-extremal black-hole configurations, identifying a two-branch structure (abelian and non-abelian) and deriving the Hawking-temperature behavior of the horizons. A key finding is that the confinement/chiral-breaking scale coincides with the Hagedorn temperature of the little string theory, while the canonical ensemble is thermodynamically unstable due to negative specific heat, implying subtle UV/massive-mode couplings and potential Gregory–Laflamme-type instabilities. In certain limits they obtain explicit non-linear sigma models with a linear dilaton and a simple Abelian solution with a NS-NS coset sigma-model counterpart, suggesting connections to exact world-sheet CFTs. Overall, the work sheds light on how UV completions (little string theory) influence low-energy gauge dynamics in holographic confining backgrounds and highlights the nuanced thermodynamics of wrapped 5-brane constructions.

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.

Paper Structure

This paper contains 11 sections, 91 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Summary of results
  3. Organization of the paper
  4. Ten-dimensional description of 5-branes on $S^2$
  5. $D=4$ description: non-Abelian black holes in gauged ${\cal N}=4$ supergravity
  6. Extremal solutions
  7. BPS solutions
  8. Non-BPS solutions
  9. Vanishing gauge field ($w=\pm 1$)
  10. Special Abelian solution ($w=0,\ g=0$) and its NS-NS coset sigma model counterpart
  11. Globally regular solutions

Figures (1)

  • Figure :