Quantum Liouville theory and BTZ black hole entropy

In this paper I give an explicit conformal field theory description of (2+1)-dimensional BTZ black hole entropy. In the boundary Liouville field theory I investigate the reducible Verma modules in the elliptic sector, which correspond to certain irreducible representations of the quantum algebra U_q(sl_2) \odot U_{\hat{q}}(sl_2). I show that there are states that decouple from these reducible Verma modules in a similar fashion to the decoupling of null states in minimal models. Because ofthe nonstandard form of the Ward identity for the two-point correlation functions in quantum Liouville field theory, these decoupling states have positive-definite norms. The explicit counting from these states gives the desired Bekenstein-Hawking entropy in the semi-classical limit when q is a root of unity of odd order.Comment: LaTeX, 33 pages, 4 eps figure

Unbounded violation of tripartite Bell inequalities

We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model. This is in sharp contrast with the bipartite case, where all violations are bounded by Grothendieck's constant. We will discuss the possibility of determining the Hilbert space dimension from the obtained violation and comment on implications for communication complexity theory. Moreover, we show that the violation obtained from generalized GHZ states is always bounded so that, in contrast to many other contexts, GHZ states do in this case not lead to extremal quantum correlations. The results are based on tools from the theories of operator spaces and tensor norms which we exploit to prove the existence of bounded but not completely bounded trilinear forms from commutative C*-algebras.Comment: Substantial changes in the presentation to make the paper more accessible for a non-specialized reade