Exact Path Integral For 3D Quantum Gravity. Ii.

Masazumi Honda, Norihiro Iizuka, Akinori Tanaka, Seiji Terashima

Research output: Contribution to journalArticlepeer-review


Continuing the work [Phys. Rev. Lett. 115, 161304 (2015)], we discuss various aspects of three-dimensional quantum gravity partition function in anti-de Sitter spacetime in the semiclassical limit. The partition function is holomorphic and is the one which we obtained by using the localization technique of Chern-Simons theory in Phys. Rev. Lett. 115, 161304 (2015). We obtain a good expression for it in the summation form over Virasoro characters for the vacuum and primaries. A key ingredient for that is an interpretation of boundary-localized fermion. We also check that the coefficients in the summation form over Virasoro characters of the partition function are positive integers and satisfy the Cardy formula. These give a physical interpretation that these coefficients represent the number of primary fields in the dual conformal field theory in the large k limit.
Original languageEnglish
Article number064014
Number of pages5
JournalPhysical Review D
Issue number6
StatePublished - Mar 2016


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