One-loop partition functions of 3D gravity

Simone Giombi, Alexander Maloney, Xi Yin

Research output: Contribution to journalArticlepeer-review

177 Scopus citations


We consider the one-loop partition function of free quantum field theory in locally Anti-de Sitter space-times. In three dimensions, the one loop determinants for scalar, gauge and graviton excitations are computed explicitly using heat kernel techniques. We obtain precisely the result anticipated by Brown and Henneaux: the partition function includes a sum over ''boundary excitations'' of AdS 3, which are the Virasoro descendants of empty Anti-de Sitter space. This result also allows us to compute the one-loop corrections to the Euclidean action of the BTZ black hole as well its higher genus generalizations.

Original languageEnglish (US)
Article number007
JournalJournal of High Energy Physics
Issue number8
StatePublished - Aug 1 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • AdS-CFT correspondence
  • Black holes
  • Models of quantum gravity


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