$ {{\mathcal{W}}_3} $ irregular states and isolated $ \mathcal{N}=2 $ superconformal field theories

Abstract

We explore the proposal that the six-dimensional (2, 0) theory on the Riemann surface with irregular punctures leads to a four-dimensional gauge theory coupled to the isolated $ \mathcal{N}=2 $ superconformal theories of Argyres-Douglas type, and to two-dimensional conformal field theory with irregular states. Following the approach of Gaiotto-Teschner for the Virasoro case, we construct $ {{\mathcal{W}}_3} $ irregular states by colliding a single SU(3) puncture with several regular punctures of simple type. If n simple punctures are colliding with the SU(3) puncture, the resulting irregular state is a simultaneous eigenvector of the positive modes L n , . . . , L 2n and W 2n , . . . , W 3n of the $ {{\mathcal{W}}_3} $ algebra. We find the corresponding isolated SCFT with an SU(3) flavor symmetry as a nontrivial IR fixed point on the Coulomb branch of the SU(3) linear quiver gauge theories, by confirming that its Seiberg-Witten curve correctly predicts the conditions for the $ {{\mathcal{W}}_3} $ irregular states. We also compare these SCFT’s with the ones obtained from the BPS quiver method.