New 1/N expansions in random tensor models

Valentin Bonzom

doi:10.1007/jhep06(2013)062

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arXiv · 1211.1657

New 1/N expansions in random tensor models

Valentin Bonzom

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Abstract

Although random tensor models were introduced twenty years ago, it is only in 2011 that Gurau proved the existence of a 1/N expansion. Here we show that there actually is more than a single 1/N expansion, depending on the dimension. These new expansions can be used to define tensor models for `rectangular' tensors (whose indices have different sizes). In the large N limit, they retain more than the melonic graphs. Still, in most cases, the large N limit is found to be Gaussian, and therefore extends the scope of the universality theorem for large random tensors. Nevertheless, a scaling which leads to non-Gaussian large N limits, in even dimensions, is identified for the first time.

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Valentin Bonzom. 2012-11-07. New 1/N expansions in random tensor models. https://doi.org/10.1007/jhep06(2013)062

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