A Local Logarithmic Conformal Field Theory

TL;DR

Gaberdiel and Kausch construct a local logarithmic CFT associated with the triplet algebra at $c=-2$, demonstrating locality and crossing symmetry allow a consistent, non-chiral theory with a modular invariant spectrum. They determine the finite spectrum, derive two-, three-, and some four-point amplitudes, and show the partition function $Z$ is modular invariant and matches a circle compactification at radius $R= ext{√}2$, though the non-chiral sector is a quotient rather than a simple tensor product. The construction is realized by a quotient of reducible left-right sectors to enforce locality, and is shown to be equivalent to the bosonic sector of a free symplectic-fermion theory, providing the first explicit non-chiral rational LCFT. This work thus shows that logarithmic CFTs can define fully consistent conformal field theories with nontrivial global structure, extending the landscape beyond chiral theories.

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.