From SO/Sp instantons to W-algebra blocks

TL;DR

This paper explores instanton partition functions for specific superconformal gauge theories, revealing their relations through geometric mappings and establishing an AGT-type correspondence with W-algebra blocks, simplifying previous U(1) factor issues.

Contribution

It introduces a new AGT-type correspondence for Sp(1)/SO(4) theories with W(2,2)-algebra symmetry, connecting instanton functions via geometric double coverings.

Findings

Agreement of instanton partition functions after coupling mapping

Formulation of an AGT-type correspondence with W(2,2)-algebra

Explicit computation for linear quivers confirming the correspondence

Abstract

We study instanton partition functions for N=2 superconformal Sp(1) and SO(4) gauge theories. We find that they agree with the corresponding U(2) instanton partitions functions only after a non-trivial mapping of the microscopic gauge couplings, since the instanton counting involves different renormalization schemes. Geometrically, this mapping relates the Gaiotto curves of the different realizations as double coverings. We then formulate an AGT-type correspondence between Sp(1)/SO(4) instanton partition functions and chiral blocks with an underlying W(2,2)-algebra symmetry. This form of the correspondence eliminates the need to divide out extra U(1) factors. Finally, to check this correspondence for linear quivers, we compute expressions for the Sp(1)-SO(4) half-bifundamental.