Continuous Symmetries of Lattice Conformal Field Theories and their $Z_2$-Orbifolds

TL;DR

This paper investigates the continuous symmetries of lattice-based conformal field theories and their $Z_2$-orbifolds, confirming that these symmetries are generated by vertex operator modes under certain conditions.

Contribution

It demonstrates that the expected inner symmetries are generated by vertex operator modes and proposes a criterion for this to hold generally.

Findings

Inner symmetries are generated by vertex operator modes

A criterion for symmetry generation is proposed

The results apply to lattice conformal field theories and their orbifolds

Abstract

Following on from a general observation in an earlier paper, we consider the continuous symmetries of a certain class of conformal field theories constructed from lattices and their reflection-twisted orbifolds. It is shown that the naive expectation that the only such (inner) symmetries are generated by the modes of the vertex operators corresponding to the states of unit conformal weight obtains, and a criterion for this expectation to hold in general is proposed.