A Local Logarithmic Conformal Field Theory

TL;DR

This paper constructs a non-chiral rational logarithmic conformal field theory at c=-2, demonstrating its modular invariance and establishing it as a valid conformal field theory model.

Contribution

It provides the first explicit construction of a non-chiral rational logarithmic conformal field theory, detailing its spectrum, amplitudes, and symmetry properties.

Findings

The theory is modular invariant.

A consistent set of amplitudes satisfying locality and crossing symmetry is found.

The spectrum of the theory is explicitly determined.

Abstract

The local logarithmic conformal field theory corresponding to the triplet algebra at c=-2 is constructed. The constraints of locality and crossing symmetry are explored in detail, and a consistent set of amplitudes is found. The spectrum of the corresponding theory is determined, and it is found to be modular invariant. This provides the first construction of a non-chiral rational logarithmic conformal field theory, establishing that such models can indeed define bona fide conformal field theories.