We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two– and three– point functions. This calculation is done for the general case of more than one logarithmic field in a block, and more than one set of logarithmic fields. Then we show that one can regard the logarithmic field as a formal derivative of the ord...

In this paper we study how the exact nonperturbative integrability methods in $4D$ $\mathcal{N}=4$ super-Yang-Mills can work efficiently together with numerical conformal bootstrap techniques to go beyond spectral observables and access previously unreachable quantities such as correlation functions at finite coupling. setup of 1D defect field theory living on a Maldacena-Wilson line, managed c...

String backgrounds are described as purely geometric objects related to moduli spaces of Riemann surfaces, in the spirit of Segal’s definition of a conformal field theory. Relations with conformal field theory, topological field theory and topological gravity are studied. For each field theory, an algebraic counterpart, the (homotopy) algebra satisfied by the tree level correlators, is construc...

We show that the fusion rule for a modular invariant Ertype conformal field theory, which is constructed from the one for the A,(l) Kac-Moody algebra by naive extension, is not associative. Then by imposing .further restrictions to this naive fusion rule, we obtain associative fusion rules for the E7-type conformal field theory. Unlike the case of an E6-type conformal field theory, these fusion...