New 1/N expansions in random tensor models

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.

18 pages, 13 figures. v2: more figures, and 1/N expansions for rectangular tensors

References in corpus (3)

• Random tensor models in the large N limit: Uncoloring the colored tensor models
• The 1/N expansion of colored tensor models
• Revisiting random tensor models at large N via the Schwinger-Dyson equations

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