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Branched Matrix Models and the Scales of Supersymmetric Gauge Theories | | Marco Matone
; Luca Mazzucato
; | | Date: |
26 May 2003 | | Journal: | JHEP 0307 (2003) 015 | | Subject: | hep-th hep-ph | | Abstract: | In the framework of the matrix model/gauge theory correspondence, we consider supersymmetric U(N) gauge theory with $U(1)^N$ symmetry breaking pattern. Due to the presence of the Veneziano--Yankielowicz effective superpotential, in order to satisfy the $F$--term condition $sum_iS_i=0$, we are forced to introduce additional terms in the free energy of the corresponding matrix model with respect to the usual formulation. This leads to a matrix model formulation with a cubic potential which is free of parameters and displays a branched structure. In this way we naturally solve the usual problem of the identification between dimensionful and dimensionless quantities. Furthermore, we need not introduce the $N=1$ scale by hand in the matrix model. These facts are related to remarkable coincidences which arise at the critical point and lead to a branched bare coupling constant. The latter plays the role of the $N=1$ and $N=2$ scale tuning parameter. We then show that a suitable rescaling leads to the correct identification of the $N=2$ variables. Finally, by means of the the mentioned coincidences, we provide a direct expression for the $N=2$ prepotential, including the gravitational corrections, in terms of the free energy. This suggests that the matrix model provides a triangulation of the istanton moduli space. | | Source: | arXiv, hep-th/0305225 | | Services: | Forum | Review | PDF | Favorites | |
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