On W-algebras and the symmetries of defects of 6d N=(2,0) theory

TL;DR

This paper investigates the relationship between 6d N=(2,0) theories with defects and W-algebras, providing evidence that the symmetries of defects correspond to specific W-algebra structures in lower-dimensional theories.

Contribution

It offers a verification of a conjecture linking 6d defect symmetries to W-algebras by matching the level of current subalgebras derived from defect properties.

Findings

Reproduces the level of the current subalgebra 13; of the W-algebra from defect data.

Supports the conjecture connecting 6d defect symmetries to W-algebra structures.

Provides a consistency check for the proposed duality between defects and W-algebras.

Abstract

We consider 6d N=(2,0) theory on N M5-branes, together with a 4d defect labeled by a Young diagram Y specifying its global symmetry G_Y. A recent conjecture states that a compactification of this system leads to a 2d theory with W-algebra symmetry depending on Y. We provide a check of the conjecture by reproducing the level of the current subalgebra \hat{G}_Y of this W-algebra from the property of the 4d defect.