On conformal field theories at fractional levels

TL;DR

This paper explores conformal field theories at fractional levels, providing new methods to compute conformal data using automorphisms of lattice groups and extending to affine theories, with applications to Gauss sums.

Contribution

It introduces an alternative approach to defining lattice-based conformal field theories using automorphisms, generalizes to affine theories, and computes Gauss sums for lattices.

Findings

New conformal data from automorphisms of lattice groups

Extension of methods to affine theories

Explicit computation of Gauss sums for lattices

Abstract

For each lattice one can define a free boson theory propagating on the corresponding torus. We give an alternative definition where one employs any automorphism of the group $M^*/M$. This gives a wealth of conformal data, which we realize as some bosonic theory, in all the `regular' cases. We discuss the generalization to affine theories. As a byproduct, we compute the gauss sum for any lattice and any diagonal automorphism.