Exact path integral for 3D higher spin gravity

Masazumi Honda, Norihiro Iizuka, Akinori Tanaka, Seiji Terashima

Research output: Contribution to journalArticlepeer-review


Extending the works of [Phys. Rev. Lett. 115, 161304 (2015)] and [Phys. Rev. D 93, 064014 ( 2016)], we study three dimensional Euclidean higher spin gravity with negative cosmological constant. This theory can be formulated in terms of SL(N, C) Chern-Simons theory. By introducing auxiliary fields, we rewrite it in a supersymmetric way and compute its partition function exactly by using the localization method. We obtain a good expression for the partition function in terms of characters for the vacuum and primaries in 2D unitary conformal field theory with W-N symmetry. We also check that the coefficients of the character expansion are positive integers and exhibit Cardy formula in the large central charge limit.

Original languageEnglish
Article number046016
Number of pages8
JournalPhysical Review D
Issue number4
StatePublished - 28 Feb 2017


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