The Whitham Deformation of the Dijkgraaf-Vafa Theory

Details The Whitham Deformation of the Dijkgraaf-Vafa Theory The Whitham Deformation of the Dijkgraaf-Vafa Theory

2003-09-25

arxiv.org/abs/hep-th/0309232v4

JHEP 0403:072,2004

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/1126-6708/2004/03/072

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.

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