Logarithmic torus amplitudes

TL;DR

This paper analyzes the structure of torus amplitudes in the logarithmic triplet conformal field theory at c=-2, revealing a basis formed by irreducible characters and a logarithmic extension function.

Contribution

It demonstrates that the space of torus amplitudes is spanned by irreducible characters and a logarithmic extension, providing insights into the structure of logarithmic conformal field theories.

Findings

Torus amplitude space is spanned by irreducible characters and a logarithmic extension function.

The analysis applies specifically to the c=-2 logarithmic triplet theory.

Implications for generalizations of logarithmic conformal field theories are discussed.

Abstract

For the example of the logarithmic triplet theory at c=-2 the chiral vacuum torus amplitudes are analysed. It is found that the space of these torus amplitudes is spanned by the characters of the irreducible representations, as well as a function that can be associated to the logarithmic extension of the vacuum representation. A few implications and generalisations of this result are discussed.