Random tensors, loop vertex expansion and their cumulants

By Vincent Rivasseau

Appears in collection : 2023 - T1A - WS2 - Tensor models and holography

In the first part of my talk I shall present some generalities about random tensor models in relation with quantum gravity. In the second part I introduce the loop vertex expansion which is a technique of constructive field theory. In the third part I construct cumulants of a $U(N)$ vector model perturbed by a quartic term. This model has a non-trivial covariance to allow for renormalisation, but is one the simplest models one could think of, because its renormalization is limited to tadpoles. Nevertheless it requires a different technique, the multi-scale loop vertex expansion, and for cumulants it has never been done. I prove their Borel summability in a cardioid of the associated coupling constant.

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Citation data

  • DOI 10.57987/IHP.2023.T1A.WS2.008
  • Cite this video RIVASSEAU Vincent (2/10/23). Random tensors, loop vertex expansion and their cumulants. IHP. Audiovisual resource. DOI: 10.57987/IHP.2023.T1A.WS2.008
  • URL https://dx.doi.org/10.57987/IHP.2023.T1A.WS2.008

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