Disk one-point function for non-rational conformal theories

JUAN PABLO BABARO; GASTON GIRIBET

JOURNAL OF HIGH ENERGY PHYSICS

SPRINGER

Año: 2010 vol. 1009 p. 77 - 77

1126-6708

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 [arXiv:0803.2099], are parameterized by two real numbers (b,m) in such a way that the corresponding central charges c are given by c=1+6(b+b^{-1}(1-m))^{2}. For the disk geometry, we explicitly compute the expectation value of a bulk vertex operator in the generic case m in R, such that the result trivially reduces to the Liouville one-point function when m=0. For the case m=1 the observable we compute corresponds to the one-point function in the SL(2,C}/SU(2) Wess-Zumino-Novikov-Witten theory (WZNW). In fact, our calculation mimics the analysis recently performed in [arXiv:0710.2093] for the case of the WZNW theory, showing how the boundary action for Euclidean AdS_2 D-branes in Euclidean AdS_3 space proposed therein admits a straightforward generalization to the whole family of m-parameterized non-rational models. A difference with respect to the WZNW theory arises in that, in contrast to the case m=1, the CFT defined for generic $m$ does not exhibit sl(2)_k affine Kac-Moody symmetry but a Borel subalgebra of it, and this requires to implement conformal invariant boundary condition in a sligthly different manner. 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.