Spectra of Operators in Large $N$ Tensor Models

Understand

We study the operators in the large $N$ tensor models, focusing mostly on the fermionic quantum mechanics with $O(N)^3$ symmetry which may be either global or gauged.

• In the model with global symmetry we study the spectra of bilinear operators, which are in either the symmetric traceless or the antisymmetric representation of one of the $O(N)$ groups.
• In the symmetric traceless case, the spectrum of scaling dimensions is the same as in the SYK model with real fermions; it includes the $h=2$ zero-mode.
• For the operators anti-symmetric in the two indices, the scaling dimensions are the same as in the additional sector found in the complex tensor and SYK models; the lowest $h=0$ eigenvalue corresponds to the conserved $O(N)$ charges.