The 1 / N Expansion of the Symmetric Traceless and the Antisymmetric Tensor Models in Rank Three

Dario Benedetti (1) , Sylvain Carrozza (2) , Razvan Gurau (2, 3) , Maciej Kolanowski (4)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
2 Perimeter Institute for Theoretical Physics [Waterloo]
3 CPHT - Centre de Physique Théorique [Palaiseau]
4 UW - University of Warsaw

We prove rigorously that the symmetric traceless and the antisymmetric tensor models in rank three with tetrahedral interaction admit a 1/N expansion, and that at leading order they are dominated by melon diagrams. This proves the recent conjecture of I. Klebanov and G. Tarnopolsky in [1], which they checked numerically up to 8th order in the coupling constant.

Domaines: Physique mathématique [math-ph]

Dario Benedetti, Sylvain Carrozza, Razvan Gurau, Maciej Kolanowski. The 1 / N Expansion of the Symmetric Traceless and the Antisymmetric Tensor Models in Rank Three. Communications in Mathematical Physics, 2019, 371 (1), pp.55-97. ⟨10.1007/s00220-019-03551-z⟩. ⟨hal-02356134⟩