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

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.

31 pages, 1 figure; v2: typos corrected; references, a note on Kovner-Shifman vacua (section 4.3) and a few clarifying comments in Section 3 added; v3: cosmetic changes, JHEP version

Cited by in corpus (7)

• Extended N=1 super Yang-Mills theory
• N=2 Quiver Gauge Model and Partial Supersymmetry Breaking
• The Chiral Ring and the Periods of the Resolvent
• Deformation of Dijkgraaf-Vafa Relation via Spontaneously Broken N=2 Supersymmetry II
• Consistency conditions in the chiral ring of super Yang-Mills theories
• Microscopic quantum superpotential in N=1 gauge theories
• Glueball operators and the microscopic approach to N=1 gauge theories