Wild Quiver Gauge Theories

TL;DR

This paper extends the AGT correspondence to 4d N=2 SU(2) gauge theories coupled to non-Lagrangian SCFTs arising from A1(2,0) on Riemann surfaces with irregular punctures. It formulates a gauge/CFT dictionary using irregular conformal blocks and generalized coherent states to capture the Seiberg-Witten geometry of wild quivers, framed by Hitchin systems with wild ramification. The authors explicitly construct D_n and hat_A_{m,n} theories, relate their SW curves to Hitchin data, and verify prepotentials by matching irregular blocks with the gauge theory moduli, including degenerate-field insertions that quantify Hitchin system quantization. The work lays a foundation for higher-rank generalizations and deeper links to string theory, topological strings, and holomorphic anomaly equations.

Abstract

We study N=2 supersymmetric SU(2) gauge theories coupled to non-Lagrangian superconformal field theories induced by compactifying the six dimensional A_1 (2,0) theory on Riemann surfaces with irregular punctures. These are naturally associated to Hitchin systems with wild ramification whose spectral curves provide the relevant Seiberg-Witten geometries. We propose that the prepotential of these gauge theories on the Omega-background can be obtained from the corresponding irregular conformal blocks on the Riemann surfaces via a generalization of the coherent state construction to the case of higher order singularities.