Stress Energy tensor in LCFT and the Logarithmic Sugawara construction

TL;DR

This paper explores the structure of the stress energy tensor and its logarithmic partners in LCFTs, introducing a generalized Sugawara construction to compute these partners, especially in the c=-2 theory.

Contribution

It presents a novel generalized Sugawara construction method for calculating logarithmic partners of the stress energy tensor in LCFTs.

Findings

The construction applies to the c=-2 theory with primary currents.

It distinguishes between theories with zero and non-zero central charge.

The method reveals the structure of logarithmic extensions of Kac-Moody algebra.

Abstract

We discuss the partners of the stress energy tensor and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. However they are both characterised by at least two independent parameters. We show how, by using a generalised Sugawara construction, one can calculate the logarithmic partner of T. We show that such a construction works in the c=-2 theory using the conformal dimension one primary currents which generate a logarithmic extension of the Kac-Moody algebra.