Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models

Abstract

This is a semi-pedagogical review of a medium size on the exact determination of and the role played by the low energy effective prepotential $\mathcal{F}$ in QFT with (broken) extended supersymmetry, which began with the work of Seiberg and Witten in 1994. While paying an attention to an overall view of this subject lasting long over the two decades, we probe several corners marked in the three major stages of the developments, emphasizing uses of the deformation theory on the attendant Riemann surface as well as its close relation to matrix models. Examples picked here in different contexts tell us that the effective prepotential is to be identified as the suitably defined free energy $F$ of a matrix model: $\mathcal{F}=F$. To be submitted to PTEP as an invited review article and based in part on the talk delivered by one of the authors (H.I.) in the workshop held at Shizuoka University, Shizuoka, Japan, on December 5, 2014.

60 pages, 5 figures, to be submitted to PTEP as an invited review article and based in part on the talk delivered by one of the authors (H.I.) in the workshop held at Shizuoka University, Shizuoka, Japan, on December 5, 2014; v2: minor corrections, references added

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Cited by in corpus (11)

• Ward identities and combinatorics of rainbow tensor models
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• A slow review of the AGT correspondence
• Discrete Painleve system and the double scaling limit of the matrix model for irregular conformal block and gauge theory
• Classical limit of irregular blocks and Mathieu functions
• q-Vertex Operator from 5D Nekrasov Function
• N=2 gauge theories, instanton moduli spaces and geometric representation theory
• Localization principle in SUSY gauge theories
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Construction of irregular conformal/W block and flavor mass relations of $\mathcal{N}=2$ SUSY gauge theory from the $A_{n-1}$ quiver matrix model
• Theory space of one unitary matrix model and its critical behavior associated with Argyres-Douglas theory