The Microscopic Approach to N=1 Super Yang-Mills Theories

TL;DR

This paper develops a microscopic formalism for N=1 super Yang-Mills theories using Nekrasov's instanton technology, enabling computation of chiral observables and establishing equivalence with matrix model approaches.

Contribution

It introduces a first-principle method for calculating observables in N=1 theories and proves the equivalence with the Dijkgraaf-Vafa matrix model framework.

Findings

Formalism computes chiral correlators in strongly coupled vacua.

Results match the Dijkgraaf-Vafa matrix model approach.

Establishes open/closed string duality in the chiral sector.

Abstract

We give a brief account of the recent progresses in super Yang-Mills theories based in particular on the application of Nekrasov's instanton technology to the case of N=1 supersymmetry. We have developed a first-principle formalism from which any chiral observable in the theory can be computed, including in strongly coupled confining vacua. The correlators are first expressed in terms of some external variables as sums over colored partitions. The external variables are then fixed to their physical values by extremizing the microscopic quantum superpotential. Remarquably, the results can be shown to coincide with the Dijkgraaf-Vafa matrix model approach, which uses a totally different mathematical framework. These results clarify many important properties of N=1 theories, related in particular to generalized Konishi anomaly equations and to Veneziano-Yankielowicz terms in the glueball superpotentials. The proof of the equivalence between the formalisms based on colored partitions and on matrices is also a proof of the open/closed string duality in the chiral sector of the theories.