W_3 irregular states and isolated N=2 superconformal field theories

TL;DR

This paper constructs W_3 irregular states from colliding punctures in 2D CFT, linking them to isolated N=2 superconformal theories and confirming their properties via Seiberg-Witten curves and BPS quivers.

Contribution

It introduces a method to construct W_3 irregular states through puncture collisions and connects these states to isolated N=2 superconformal theories in four dimensions.

Findings

Constructed W_3 irregular states from colliding punctures.

Identified corresponding isolated SCFTs with SU(3) flavor symmetry.

Confirmed SCFT properties using Seiberg-Witten curves and BPS quiver analysis.

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 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 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 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 W_3 irregular states. We also compare these SCFT's with the ones obtained from the BPS quiver method.