Exact path integral for 3D higher spin gravity

Masazumi Honda, Norihiro Iizuka, Akinori Tanaka, Seiji Terashima
2017 Physical Review D  
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
more » ... h 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.
doi:10.1103/physrevd.95.046016 fatcat:uzq5mmk6tfd4tpzkrhti2ketvq