The Proof of the Dijkgraaf-Vafa Conjecture and application to the mass gap and confinement problems

TL;DR

This paper proves the Dijkgraaf-Vafa conjecture by showing how gauge invariance and anomaly equations determine key constants, leading to new insights into mass gap and confinement in super Yang-Mills theories.

Contribution

It provides a rigorous proof of the Dijkgraaf-Vafa conjecture and applies it to address fundamental problems in supersymmetric gauge theories.

Findings

Constants in chiral operator expectation values are fully determined by gauge invariance and anomalies.

The extremization of the Dijkgraaf-Vafa superpotential unambiguously fixes all terms.

New results on mass gap and confinement in super Yang-Mills theories.

Abstract

Using generalized Konishi anomaly equations, it is known that one can express, in a large class of supersymmetric gauge theories, all the chiral operators expectation values in terms of a finite number of a priori arbitrary constants. We show that these constants are fully determined by the requirement of gauge invariance and an additional anomaly equation. The constraints so obtained turn out to be equivalent to the extremization of the Dijkgraaf-Vafa quantum glueball superpotential, with all terms (including the Veneziano-Yankielowicz part) unambiguously fixed. As an application, we fill non-trivial gaps in existing derivations of the mass gap and confinement properties in super Yang-Mills theories.