The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory

TL;DR

This paper explores the Dijkgraaf-Vafa prepotential as a specific example within Seiberg-Witten theory, emphasizing the importance of a complete moduli system and the role of WDVV equations, while proposing a regularized framework.

Contribution

It introduces the concept of a regularized DV system and discusses its properties in the context of Seiberg-Witten theory, highlighting the moduli extension and WDVV equations.

Findings

WDVV equations hold before regularization is lifted

Complete moduli include sizes and positions of cuts

Regularized DV system generalizes matrix model interpretation

Abstract

We consider the prepotential of Dijkgraaf and Vafa (DV) as one more (and in fact, singular) example of the Seiberg-Witten (SW) prepotentials and discuss its properties from this perspective. Most attention is devoted to the issue of complete system of moduli, which should include not only the sizes of the cuts (in matrix model interpretation), but also their positions, i.e. the number of moduli should be almost doubled, as compared to the DV consideration. We introduce the notion of regularized DV system (not necessarilly related to matrix model) and discuss the WDVV equations. These definitely hold before regularization is lifted, but an adequate limiting procedure, preserving all ingredients of the SW theory, remains to be found.