Conical spaces, modular invariance and cp,1 holography

We propose a non-unitary example of holography for the family of two-dimensional logarithmic conformal field theories with negative central charge c = c(p,1) = -6p + 13 - 6p(-1). We argue that at large p, these models have a semiclassical gravity-like description which contains, besides the global AdS(3) 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 c(p,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.

Automated summary

We propose a non-unitary holographic example for the family of two-dimensional logarithmic conformal field theories, where the central charge and the natural modular invariant partition function coincide with those of the related model. These models exhibit a semiclassical gravity-like description at large p values, containing the global AdS(3) spacetime and solitonic solutions describing conical excess angles. Close examination reveals a direct link between geometric actions for exceptional Virasoro coadjoint orbits and Felder's free field construction of degenerate representations.