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

TL;DR

This work tests a conjecture that compactifying the 6d $\mathcal{N}=(2,0)$ theory with codimension-two defects labeled by a Young diagram $Y$ yields a 2d theory with a $W$-algebra symmetry tied to $Y$. By computing and matching anomaly data from the 4d defect and the 11d supergravity dual, the author shows that the levels of the $\hat{G}_Y$ current subalgebras in the $W$-algebra are $k_i = -\lambda_{\eta_i}-\eta_i b^2$ with $b^2=\epsilon_2/\epsilon_1$, in agreement with the compactification picture. This provides a nontrivial check of the proposed Drinfeld-Sokolov reduction structure governing the 2d symmetry and clarifies the interplay between the defect data, the 4d anomalies, and the 2d W-algebra. The results cement the link between 6d defect data, anomaly inflow, and emergent 2d chiral algebras, and point toward broader explorations of full anomaly polynomials and extensions to other ADE types.

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.

Figures (3)

• Figure 1: A Young diagram and various sequences associated to it.
• Figure 2: Quiver tail corresponding to the Young diagram in Fig. \ref{['young']}.
• Figure 3: Graph of $\lambda(\eta)$ for the Young diagram given in Fig. \ref{['young']}. The slope of the function changes discontinuously at the black points shown.