Toda Theory From Six Dimensions

Abstract

We describe a compactification of the six-dimensional (2,0) theory on a four-sphere which gives rise to a two-dimensional Toda theory at long distances. This construction realizes chiral Toda fields as edge modes trapped near the poles of the sphere. We relate our setup to compactifications of the (2,0) theory on the five and six-sphere. In this way, we explain a connection between half-BPS operators of the (2,0) theory and two-dimensional W-algebras, and derive an equality between their conformal anomalies. As we explain, all such relationships between the six-dimensional (2,0) theory and Toda field theory can be interpreted as statements about the edge modes of complex Chern-Simons on various three-manifolds with boundary.

40 pages, 2 figures

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• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• 6d (2,0) and M-theory at 1-loop
• Quantizing higher-spin gravity in free-field variables
• Perturbative and nonperturbative aspects of complex Chern-Simons Theory
• A brief review of the 2d/4d correspondences
• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• An $\mathcal{N}=1$ 3d-3d Correspondence
• M5 branes and Theta Functions
• $\mathcal{N}=(1,0)$ Anomaly Multiplet Relations in Six Dimensions
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• Comments on chiral algebras and $\Omega$-deformations
• Abelian M5-brane on $S^6$
• Dual infrared limits of 6d $\mathcal{N}$=(2,0) theory
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories