Para-Liouville/Toda central charges from M5-branes

TL;DR

This paper proposes a new connection between M5-branes on specific orbifolds and 2D theories with complex symmetries, supported by central charge calculations from anomaly polynomials.

Contribution

It introduces a novel correspondence between M5-branes on R^4/Z_m and 2D theories with SU(m)_N and para-W_N symmetries, extending known symmetries.

Findings

Derived the central charge of the 2D theory from the 6D anomaly polynomial.

Identified the symmetry structures for special cases m=1 and N=2.

Supported the proposal with consistency checks.

Abstract

We propose that N M5-branes, put on R^4/Z_m with deformation parameters epsilon_{1,2}, realize two-dimensional theory with SU(m)_N symmetry and m-th para-W_N symmetry. This includes the standard W_N symmetry for m=1 and super-Viraroro symmetry for m=N=2. We provide a small check of this proposal by calculating the central charge of the 2d theory from the anomaly polynomial of the 6d theory.