Disk one-point function for a family of non-rational conformal theories

Abstract

We consider an infinite family of non-rational conformal field theories in the presence of a conformal boundary. These theories, which have been recently proposed in [1], are parameterized by two real numbers (b,m) in such a way that the corresponding central charges c (b,m) are given by c (b,m) = 3+6(b+b -1(1-m)) 2. For the disk geometry, we explicitly compute the expectation value of a bulk vertex operator in the case m ∈ ℤ, such that the result reduces to the Liouville one-point function when m = 0. We perform the calculation of the disk one-point function in two different ways, obtaining results in perfect agreement, and giving the details of both the path integral and the free field derivations. © SISSA 2010.