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- New limits for large N matrix and tensor models

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19120010

In this talk, I will describe the framework of large D matrix models, which provides new limits for matrix models where the sum over planar graphs simplifies when D is large. The basic degrees of freedom are a set of D real matrices of size NxN which is invariant under O(D). These matrices can be naturally interpreted as a real tensor of rank three, making a compelling connection with tensor models. Furthermore, they have a natural interpretation in terms of D-brane constructions in string theory. I will present a way to define a large D scaling of the coupling constants such that the sum over Feynman graphs of fixed genus in matrix models admits a well-defined large D expansion. In particular, in the large D limit, the sum over planar graphs truncates to a tractable, yet non-trivial, sum over generalized melonic graphs. This family of graphs has been shown to display very interesting properties, especially in the case of quantum mechanical models such as the SYK model and SYK-like tensor models. If time allows, I will also explain how one can use the large D limit of matrix models to simplify the sum over all genera, which is notoriously divergent.

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©2012 Institut Périmètre de Physique Théorique