2024 - PC2 - Random tensors and related topics

Collection 2024 - PC2 - Random tensors and related topics

Organisateur(s) Collins, Benoit ; Dartois, Stéphane ; Lancien, Cécilia ; Lionni, Luca
Date(s) 30/09/2024 - 18/10/2024
URL associée https://indico.math.cnrs.fr/event/9889/
2 19

From O(N)^3 to SO(3) in tensor models

De Dario Benedetti

In this talk we consider the mean field equations of a bosonic tensor model with quartic interactions and O(N)3 symmetry. For N different from 3, their nontrivial solutions necessarily represent possible patterns of spontaneous breaking of the O(N)3 symmetry down to a proper subgroup. Besides less interesting low-rank solutions, we find one explicit solution with SO(3) invariance, for which the tensor field is expressed in terms of the Wigner 3jm symbol, highlighting an intriguing link between tensor models and SO(3) recoupling theory.

Moreover, such solution provides a tantalizing relation between different models sharing a similar large-N limit: models in which random tensors appear as fundamental variables (tensor models), models in which they appear as random couplings (p-spin and SYK models), and the Amit-Roginsky model, in which a cubic interaction is mediated by a Wigner 3jm symbol.

Informations sur la vidéo

Données de citation

  • DOI 10.57987/IHP.2024.PC2.002
  • Citer cette vidéo Benedetti, Dario (14/10/2024). From O(N)^3 to SO(3) in tensor models. IHP. Audiovisual resource. DOI: 10.57987/IHP.2024.PC2.002
  • URL https://dx.doi.org/10.57987/IHP.2024.PC2.002

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