From O(N)^3 to SO(3) in tensor models
Appears in collection : 2024 - PC2 - Random tensors and related topics
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.
