Alejandra Castro, Eliot Hijano, Arnaud Lepage-Jutier
We study SL(N,R) Chern-Simons gauge theories in three dimensions. The choice
of the embedding of SL(2,R) in SL(N,R), together with asymptotic boundary
conditions, defines a theory of higher spin gravity. Each inequivalent
embedding leads to a different asymptotic symmetry group, which we map to an
OPE structure at the boundary. A simple inspection of these algebras indicates
that only the W_N algebra constructed using the principal embedding could admit
a unitary representation for large values of the central charge.
View original:
http://arxiv.org/abs/1202.4467
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