### Abstract

In the three-dimensional sl(N) Chern-Simons higher-spin theory, we prove that the conical surplus and the black hole solution are related by the S-transformation of the modulus of the boundary torus. Then applying the modular group on a given conical surplus solution, we generate a 'SL(2, ℤ)' family of smooth constant solutions. We then show how these solutions are mapped into one another by coordinate transformations that act non-trivially on the homology of the boundary torus. After deriving a thermodynamics that applies to all the solutions in the 'SL(2, ℤ)' family, we compute their entropies and free energies, and determine how the latter transform under the modular transformations. Summing over all the modular images of the conical surplus, we write down a (tree-level) modular invariant partition function.

Original language | English |
---|---|

Article number | 94 |

Journal | Journal of High Energy Physics |

Volume | 2013 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2013 Dec |

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### Keywords

- AdS-CFT correspondence
- Black holes in string theory

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2013*(12), [94]. https://doi.org/10.1007/JHEP12(2013)094

**Modular properties of 3D higher spin theory.** / Li, Wei; Lin, Feng Li; Wang, Chih Wei.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2013, no. 12, 94. https://doi.org/10.1007/JHEP12(2013)094

}

TY - JOUR

T1 - Modular properties of 3D higher spin theory

AU - Li, Wei

AU - Lin, Feng Li

AU - Wang, Chih Wei

PY - 2013/12

Y1 - 2013/12

N2 - In the three-dimensional sl(N) Chern-Simons higher-spin theory, we prove that the conical surplus and the black hole solution are related by the S-transformation of the modulus of the boundary torus. Then applying the modular group on a given conical surplus solution, we generate a 'SL(2, ℤ)' family of smooth constant solutions. We then show how these solutions are mapped into one another by coordinate transformations that act non-trivially on the homology of the boundary torus. After deriving a thermodynamics that applies to all the solutions in the 'SL(2, ℤ)' family, we compute their entropies and free energies, and determine how the latter transform under the modular transformations. Summing over all the modular images of the conical surplus, we write down a (tree-level) modular invariant partition function.

AB - In the three-dimensional sl(N) Chern-Simons higher-spin theory, we prove that the conical surplus and the black hole solution are related by the S-transformation of the modulus of the boundary torus. Then applying the modular group on a given conical surplus solution, we generate a 'SL(2, ℤ)' family of smooth constant solutions. We then show how these solutions are mapped into one another by coordinate transformations that act non-trivially on the homology of the boundary torus. After deriving a thermodynamics that applies to all the solutions in the 'SL(2, ℤ)' family, we compute their entropies and free energies, and determine how the latter transform under the modular transformations. Summing over all the modular images of the conical surplus, we write down a (tree-level) modular invariant partition function.

KW - AdS-CFT correspondence

KW - Black holes in string theory

UR - http://www.scopus.com/inward/record.url?scp=84896343634&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896343634&partnerID=8YFLogxK

U2 - 10.1007/JHEP12(2013)094

DO - 10.1007/JHEP12(2013)094

M3 - Article

AN - SCOPUS:84896343634

VL - 2013

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 12

M1 - 94

ER -