Asymptotically free N=2 theories and irregular conformal blocks

TL;DR

This work generalizes the AGT correspondence to asymptotically free N=2 SU(2) gauge theories by constructing irregular conformal blocks from Virasoro eigenstates tied to irregular punctures of the Seiberg-Witten quadratic differential φ2. By analyzing multiple six-dimensional realizations and imposing specific eigenvalue-like conditions, the authors reproduce the corresponding Nekrasov partition functions for Nf=0,1,2,3 (up to spurious factors) and identify q with appropriate powers of the scale Λ. A second realization for Nf=2 yields a clean match without spurious factors, supporting a broader framework for irregular blocks. The results suggest a robust, higher-degree extension of the CFT/gauge theory dictionary and motivate a conjecture on the existence and uniqueness of these irregular states.

Abstract

A surprising connection between N=2 gauge theory instanton partition functions and conformal blocks has been recently proposed. We illustrate through simple examples the generalization to asymptotically free N=2 gauge theories