Modular properties of 3D higher spin theory

Wei Li, Feng Li Lin, Chih Wei Wang

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


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 languageEnglish
Article number94
JournalJournal of High Energy Physics
Issue number12
Publication statusPublished - 2013 Dec


  • AdS-CFT correspondence
  • Black holes in string theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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