Notes on melonic O(N)q−1 tensor models

Abstract

It has recently been demonstrated that the large N limit of a model of fermions charged under the global/gauge symmetry group O(N ) q−1 agrees with the large N limit of the SYK model. In these notes we investigate aspects of the dynamics of the O(N ) q−1 theories that differ from their SYK counterparts. We argue that the spectrum of fluctuations about the finite temperature saddle point in these theories has (q −1) N 2 2 new light modes in addition to the light Schwarzian mode that exists even in the SYK model, suggesting that the bulk dual description of theories differ significantly if they both exist. We also study the thermal partition function of a mass deformed version of the SYK model. At large mass we show that the effective entropy of this theory grows with energy like E ln E (i.e. faster than Hagedorn) up to energies of order N 2 . The canonical partition function of the model displays a deconfinement or Hawking Page type phase transition at temperatures of order 1/ ln N . We derive these results in the large mass limit but argue that they are qualitatively robust to small corrections in J/m.

Hints of unitarity at large N in the O(N )3 tensor field theory

“…Tensor models were initially studied in zero dimension in the context of quantum gravity and random geometry [3,[14][15][16][17]. They were then studied in one dimension [18][19][20][21][22][23][24][25][26][27][28][29][30] (see also [4,31] for reviews) as a generalization of the Sachdev-Ye-Kitaev model [32][33][34][35][36][37] without quenched disorder.…”

Matrix ensembles with global symmetries and ’t Hooft anomalies from 2d gauge theory

“…Another motivation is to explore the effect of 't Hooft anomalies in random matrix theory. Finally, we expect that aspects of this setup (although not the exact connection to random matrix theory) will be relevant for the bulk description of SYK-like theories with global symmetry [28][29][30][31][32][33][34][35].…”

SO(3) -invariant phase of the O(N)3Benedetti1, Costa2 2020Phys. Rev. D120110View full textAdd to dashboardCite

“…For the latter, we have employed the 2PI version, which is well suited to the large-N limit of vector and tensor models [21], but which is of course equivalent to the more usual 1PI effective action, once the Schwinger-Dyson equations for the two-point function are used. An interesting feature of the SO(3)-invariant solution is that it satisfies the scaling relations in equations (10)(11)(12), implying that all three quartic interactions contribute at the same order in N to the action and the field equations. In order to fully appreciate this point, we study in App.…”