Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-09-30
JHEP 1102:004,2011
Physics
High Energy Physics
High Energy Physics - Theory
23 pages; v2: References added
Scientific paper
10.1007/JHEP02(2011)004
It has recently been argued that, classically, massless higher spin theories in AdS_3 have an enlarged W_N-symmetry as the algebra of asymptotic isometries. In this note we provide evidence that this symmetry is realised (perturbatively) in the quantum theory. We perform a one loop computation of the fluctuations for a massless spin $s$ field around a thermal AdS_3 background. The resulting determinants are evaluated using the heat kernel techniques of arXiv:0911.5085. The answer factorises holomorphically, and the contributions from the various spin $s$ fields organise themselves into vacuum characters of the W_N symmetry. For the case of the hs(1,1) theory consisting of an infinite tower of massless higher spin particles, the resulting answer can be simply expressed in terms of (two copies of) the MacMahon function.
Gaberdiel Matthias R.
Gopakumar Rajesh
Saha Arunabha
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