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

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

2005-04-20

arxiv.org/abs/hep-th/0504162v2

JHEP 0510:032,2005

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, 1 figure; v2: a note and a reference added, typos corrected

Scientific paper

10.1088/1126-6708/2005/10/032

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.

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