General Virasoro Construction on Orbifold Affine Algebra

TL;DR

This work generalizes the Virasoro master equation to orbifold affine algebras at integer order $\lambda$, producing the orbifold Virasoro master equation (OVME) that reduces to the VME at $\lambda=1$ and yields extensive families of stress tensors in twisted sectors. By formulating $\hat{T}(z)=\sum_{r=0}^{\lambda-1}{\mathcal{L}}_r^{ab}:\hat{J}_a^{(r)}(z)\hat{J}_b^{(-r)}(z):$ and enforcing Virasoro symmetry, the OVME reveals a rich landscape of solutions, including cyclic constructions, subalgebra constructions, cosets, and nests, as well as novel unitary irrational central charges and ground-state weights for higher $\lambda$. The paper also introduces group-invariant (Lie) $g$-invariant constructions, demonstrates their proliferation with $\lambda$, and discusses covariance properties such as K-conjugation and Aut$(\mathbb{Z}_\lambda)$ invariances, along with several deformation schemes and the concept of the doubly-twisted affine algebra. These results extend the toolkit for constructing and classifying conformal field theories in orbifold settings and highlight potentially new, nonconventional sectors beyond standard orbifold interpretations.

Abstract

We obtain the orbifold Virasoro master equation (OVME) at integer order lambda, which summarizes the general Virasoro construction on orbifold affine algebra. The OVME includes the Virasoro master equation when lambda=1 and contains large classes of stress tensors of twisted sectors of conventional orbifolds at higher lambda. The generic construction is like a twisted sector of an orbifold (with non-zero ground state conformal weight) but new constructions are obtained for which we have so far found no conventional orbifold interpretation.