Abstract
We propose a non-unitary example of holography for the family of two-dimensional logarithmic conformal field theories with negative central charge c = cp,1 = −6p + 13 − 6p−1. We argue that at large p, these models have a semiclassical gravity-like description which contains, besides the global AdS3 spacetime, a tower of solitonic solutions describing conical excess angles. Evidence comes from the fact that the central charge and the natural modular invariant partition function of such a theory coincide with those of the cp,1 model. These theories have an extended chiral W-algebra whose currents have large spin of order |c|, and which in the bulk are realized as spinning conical solutions. As a by-product we also find a direct link between geometric actions for exceptional Virasoro coadjoint orbits, which describe fluctuations around the conical spaces, and Felder’s free field construction of degenerate representations.
Highlights
The natural guess for the modular invariant partition function under these assumptions, due to Maloney and Witten [1] and refined more recently in [2,3,4], appears not to describe a single dual theory but rather an ensemble average over CFTs
We propose a non-unitary example of holography for the family of twodimensional logarithmic conformal field theories with negative central charge c = cp,1 = −6p + 13 − 6p−1
Evidence comes from the fact that the central charge and the natural modular invariant partition function of such a theory coincide with those of the cp,1 model
Summary
Three dimensional AdS gravity can be reformulated as a Chern-Simons theory with action [31, 32]. The group PSL(2, R) ∼ SL(2, R)/Z2 consists of real 2 × 2 matrices with unit determinant, modulo the equivalence relation g ∼ −g. This Z2 quotient is important for global considerations: as it will turn out, is needed in order to allow the global AdS3 background as a nonsingular Chern-Simons configuration [16]. The Chern-Simons formulation is related to the standard formulation of gravity in terms of the vielbein ea and the spin connection (contracted with the -ymbol) ωa through. One checks that with these boundary conditions the variational principle based on (2.1) is well-defined
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