The Disc Amplitude of the Dijkgraaf-Vafa Theory:1/N Expansion vs Complex Curve Analysis

TL;DR

This paper computes the disc amplitude in the Dijkgraaf-Vafa theory using complex curve analysis, providing a systematic method to evaluate the effective superpotential for multi-cut solutions in supersymmetric QCD.

Contribution

It introduces a novel complex analysis approach to compute disc amplitudes, extending the understanding of the effective superpotential in multi-cut matrix models.

Findings

Explicit series expansion of the disc amplitude up to order S^3

Method applicable to higher orders and more complex solutions

Bridges diagrammatic and complex curve analysis methods

Abstract

According to Dijkgraaf and Vafa the effective glueball superpotential of the N=1 supersymmetric QCD coupled with an adjoint chiral multiplet is given by the planar amplitude in the 1/N expansion of a matrix model. It was shown that, when the N=1 supersymmetric QCD is coupled with fundamental chiral multiplets as well, the effective glueball superpotential is modified by the disc amplitude of the generalized matrix model. The diagramatic computation of this disc amplitude is fairly involved for the multi-cut solution. Instead we compute it with recourse to the complex analysis of the hyperelliptic curve. The result is given in series of the gluino condensation S_i. The explicit computation for the generic multi-cut solution is done up to order S^3. It is systematic so that it can be extended to higher orders.