Balasubramanian, V., de Boer, J., Feng, B., He, Y., Huang, M., Jejjala, V. & Naqvi, A. (2003). Multitrace superpotentials vs. matrix models. Communications in Mathematical Physics, 242, pp. 361392. doi: 10.1007/s0022000309479

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Abstract
We consider N = 1 supersymmetric U(N) field theories in four dimensions with adjoint chiral matter and a multitrace treelevel superpotential. We show that the computation of the effective action as a function of the glueball superfield localizes to computing matrix integrals. Unlike the singletrace case, holomorphy and symmetries do not forbid nonplanar contributions. Nevertheless, only a special subset of the planar diagrams contributes to the exact result. Some of the data of this subset can be computed from the largeN limit of an associated multitrace Matrix model. However, the prescription differs in important respects from that of Dijkgraaf and Vafa for singletrace superpotentials in that the field theory effective action is not the derivative of a multitrace matrix model free energy. The basic subtlety involves the correct identification of the field theory glueball as a variable in the Matrix model, as we show via an auxiliary construction involving a singletrace matrix model with additional singlet fields which are integrated out to compute the multitrace results. Along the way we also describe a general technique for computing the largeN limits of multitrace Matrix models and raise the challenge of finding the field theories whose effective actions they may compute. Since our models can be treated as N = 1 deformations of pure N =2 gauge theory, we show that the effective superpotential that we compute also follows from the N = 2 SeibergWitten solution. Finally, we observe an interesting connection between multitrace local theories and nonlocal field theory.
Item Type:  Article 

Additional Information:  The original publication is available at http://www.springerlink.com/content/28cj9l3h132k7127/ archiveprefix: arXiv primaryclass: hepth 
Subjects:  Q Science > QC Physics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
URI:  http://openaccess.city.ac.uk/id/eprint/841 
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