$SO(3)$-invariant phase of the $O(N)^3$ tensor model

Dario Benedetti (1) , Ilaria Costa

1 CPHT - Centre de Physique Théorique [Palaiseau]

We study classical and quantum (at large-N) field equations of bosonic tensor models with quartic interactions and O(N)3 symmetry. Among various possible patterns of spontaneous symmetry breaking we highlight an SO(3) invariant solution, with the tensor field expressed in terms of the Wigner 3jm symbol. We argue that such solution has a special role in the large-N limit, as in particular its scaling in N can provide an on-shell justification for the melonic large-N limit of the two-particle irreducible effective action in a broken phase.

Mots clés: O(N); spontaneous symmetry breaking; effective action; field equations; two-particle; scaling; Wigner; String theory; quantum gravity; gauge/gravity duality; model: tensor; boson: tensor; field theory: tensor; SO(3)

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Dario Benedetti, Ilaria Costa. $SO(3)$-invariant phase of the $O(N)^3$ tensor model. Physical Review D, 2020, 101 (8), pp.086021. ⟨10.1103/PhysRevD.101.086021⟩. ⟨hal-02440015⟩