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

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

2006-02-23

arxiv.org/abs/hep-th/0602249v3

JHEP0606:039,2006

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, 1 figure; v2: typos corrected; references, a note on Kovner-Shifman vacua (section 4.3) and a few clarifying comment

Scientific paper

10.1088/1126-6708/2006/06/039

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.

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