Coset construction of logarithmic minimal models: branching rules and branching functions

Abstract

Working in the Virasoro picture, it is argued that the logarithmic minimal models can be extended to an infinite hierarchy of logarithmic conformal field theories at higher fusion levels . From the lattice, these theories are constructed by fusing together n × n elementary faces of the appropriate models. It is further argued that all of these logarithmic theories are realized as diagonal cosets where n is the integer fusion level and is a fractional level. These cosets mirror the cosets of the higher fusion level minimal models of the form , but are associated with certain reducible representations. We present explicit branching rules for characters in the form of multiplication formulas arising in the logarithmic limit of the usual Goddard–Kent–Olive coset construction of the non-unitary minimal models . The limiting branching functions play the role of Kac characters for the theories.