SYK-like tensor quantum mechanics with Sp(N) symmetry

Abstract

We introduce a family of tensor quantum-mechanical models based on irreducible rank-3 representations of Sp(N ). In contrast to irreducible tensor models with O(N ) symmetry, the fermionic tetrahedral interaction does not vanish and can therefore support a melonic large N limit. The strongly-coupled regime has a very analogous structure as in the complex SYK model or in U(N ) × O(N ) × U(N ) tensor quantum mechanics, the main difference being that the states are now singlets under Sp(N ). We introduce character formulas that enumerate such singlets as a function of N , and compute their first values. We conclude with an explicit numerical diagonalization of the Hamiltonian in two simple examples: the symmetric model at N = 1, and the antisymmetric traceless model at N = 3.

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.…”

Sextic tensor field theories in rank 3 and 5

“…Introduction Tensor field theories are models of N r bosonic or fermionic fields with a Lagrangian invariant under U(N ) r [1], O(N ) r [2], or Sp(N ) r [3] transformations, and with r > 2. 1 Their study was initially undertaken as a generalization of matrix models in the tentative to build models of higher-dimensional quantum gravity from a geometric interpretation of their Feynman diagrams [9][10][11], but it has recently developed into new directions.…”

Line of fixed points in a bosonic tensor model

“…Tensor models have been extensively studied in zero dimensions (where they were originally introduced as models of quantum gravity [10,11], and further studied with similar motivation [12,2,13]) and in one dimension (e.g. [14,15,1,16,17,18,19,20,21,22,23], see also [24,4] for reviews) as they provide an alternative to the Sachdev-Ye-Kitaev model [25,26,27,28,29] dispensing with the quenched disorder of the latter.…”