An A_r threesome: Matrix models, 2d CFTs and 4d N=2 gauge theories

TL;DR

This paper investigates the deep connections between matrix models, 2D conformal field theories, and 4D N=2 gauge theories, highlighting their interrelations and proposing modifications for 5D instanton calculations.

Contribution

It provides a detailed comparison of A_r quiver matrix models with Toda theories and N=2 gauge theories, and proposes modifications for five-dimensional instanton partition functions.

Findings

Established correspondences between matrix models and conformal field theories.

Compared matrix model results with gauge theory quantities.

Suggested modifications for 5D instanton partition functions.

Abstract

We explore the connections between three classes of theories: A_r quiver matrix models, d=2 conformal A_r Toda field theories and d=4 N=2 supersymmetric conformal A_r quiver gauge theories. In particular, we analyse the quiver matrix models recently introduced by Dijkgraaf and Vafa and make detailed comparisons with the corresponding quantities in the Toda field theories and the N=2 quiver gauge theories. We also make a speculative proposal for how the matrix models should be modified in order for them to reproduce the instanton partition functions in quiver gauge theories in five dimensions.