Balasubramanian, V., de Boer, J., Feng, B., He, Y., Huang, M., Jejjala, V. and Naqvi, A. (2003).
Multitrace superpotentials vs. matrix models.
*Communications in Mathematical Physics*, 242,
pp. 361-392.
doi: 10.1007/s00220-003-0947-9

## Abstract

We consider N = 1 supersymmetric U(N) field theories in four dimensions with adjoint chiral matter and a multi-trace tree-level superpotential. We show that the computation of the effective action as a function of the glueball superfield localizes to computing matrix integrals. Unlike the single-trace case, holomorphy and symmetries do not forbid non-planar 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 large-N limit of an associated multi-trace Matrix model. However, the prescription differs in important respects from that of Dijkgraaf and Vafa for single-trace superpotentials in that the field theory effective action is not the derivative of a multi-trace 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 single-trace matrix model with additional singlet fields which are integrated out to compute the multi-trace results. Along the way we also describe a general technique for computing the large-N limits of multi-trace 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 Seiberg-Witten solution. Finally, we observe an interesting connection between multi-trace local theories and non-local field theory.

Publication Type: | Article |
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Additional Information: | The original publication is available at http://www.springerlink.com/content/28cj9l3h132k7127/ archiveprefix: arXiv primaryclass: hep-th |

Subjects: | Q Science > QC Physics |

Departments: | School of Mathematics, Computer Science & Engineering > Mathematics |

URI: | https://openaccess.city.ac.uk/id/eprint/841 |

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