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
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U2 - 10.1007/JHEP12(2013)094
DO - 10.1007/JHEP12(2013)094
M3 - Article
AN - SCOPUS:84896343634
SN - 1126-6708
VL - 2013
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 12
M1 - 94
ER -