The Whitham Deformation of the Dijkgraaf-Vafa Theory

Abstract

We discuss the Whitham deformation of the effective superpotential in the Dijkgraaf-Vafa (DV) theory. It amounts to discussing the Whitham deformation of an underlying (hyper)elliptic curve. Taking the elliptic case for simplicity we derive the Whitham equation for the period, which governs flowings of branch points on the Riemann surface. By studying the hodograph solution to the Whitham equation it is shown that the effective superpotential in the DV theory is realized by many different meromorphic differentials. Depending on which meromorphic differential to take, the effective superpotential undergoes different deformations. This aspect of the DV theory is discussed in detail by taking the N=1^* theory. We give a physical interpretation of the deformation parameters.

35pages, 1 figure; v2: one section added to give a physical interpretation of the deformation parameters, one reference added, minor corrections; v4: minor corrections

References in corpus (13)

• A Perturbative Window into Non-Perturbative Physics
• On Geometry and Matrix Models
• Perturbative Analysis of Gauged Matrix Models
• On Exactly Marginal Deformations of N=4 SYM and Type IIB Supergravity on AdS_5 * S^5
• Matrix models vs. Seiberg-Witten/Whitham theories
• The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
• DV and WDVV
• Exact Superpotentials from Matrix Models
• Gluino-Condensate (CIV-DV) Prepotential from its Whitham-Time Derivatives
• Seiberg--Witten Duality in Dijkgraaf--Vafa Theory
• Factorization of Seiberg-Witten Curves and Compactification to Three Dimensions
• Nonperturbative Superpotentials and Compactification to Three Dimensions
• Critical Points of Glueball Superpotentials and Equilibria of Integrable Systems

Cited by in corpus (8)

• An Introduction to Supersymmetric Gauge Theories and Matrix Models
• Partial Breaking of N=2 Supersymmetry and of Gauge Symmetry in the U(N) Gauge Model
• Supersymmetric U(N) Gauge Model and Partial Breaking of N=2 Supersymmetry
• Supersymmetric U(N) Gauge Model and Partial Breaking of N=2 Supersymmetry
• Deformation of Dijkgraaf-Vafa Relation via Spontaneously Broken N=2 Supersymmetry II
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• The Disc Amplitude of the Dijkgraaf-Vafa Theory:1/N Expansion vs Complex Curve Analysis
• Low Energy Processes Associated with Spontaneously Broken N=2 Supersymmetry