Glueball operators and the microscopic approach to N=1 gauge theories

TL;DR

This paper extends Nekrasov's microscopic approach from N=2 to N=1 gauge theories, analyzing glueball operators and non-perturbative effects, including instanton corrections and matrix model relations.

Contribution

It introduces a generalized framework for N=1 theories, detailing glueball operators and non-perturbative dynamics, building upon and extending previous N=2 methods.

Findings

Explicit calculations up to two instantons performed.

Quantum corrections to Virasoro algebra computed.

Non-perturbative analysis of Dijkgraaf-Vafa matrix model included.

Abstract

We explain how to generalize Nekrasov's microscopic approach to N=2 gauge theories to the N=1 case, focusing on the typical example of the U(N) theory with one adjoint chiral multiplet X and an arbitrary polynomial tree-level superpotential Tr W(X). We provide a detailed analysis of the generalized glueball operators and a non-perturbative discussion of the Dijkgraaf-Vafa matrix model and of the generalized Konishi anomaly equations. We compute in particular the non-trivial quantum corrections to the Virasoro operators and algebra that generate these equations. We have performed explicit calculations up to two instantons, that involve the next-to-leading order corrections in Nekrasov's Omega-background.