Exact Path Integral for 3D Higher Spin Gravity
arXiv:1511.07546 · doi:10.1103/PhysRevD.95.046016
Abstract
Extending the works arXiv:1504.05991 and arXiv:1510.02142, 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 CFT 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.
8 pages, 1 figure. v2: discussion on introducing higher-spin-charge chemical potential added
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