On Melonic Supertensor Models

TL;DR

This paper explores supersymmetric tensor models dominated by melonic diagrams, revealing a tension between supersymmetry and melonic dominance, and finds that these models flow to non-supersymmetric conformal fixed points at low energy.

Contribution

It demonstrates the incompatibility of supersymmetry with melonic dominance in tensor models and analyzes the resulting low energy conformal fixed points.

Findings

Models reach non-supersymmetric conformal fixed points

Supersymmetry breaking arises from regularization of degrees of freedom

Derived $SL(2,\mathbb{R})$ wavefunctions for fermionic excitations

Abstract

We investigate a class of supersymmetric quantum mechanical theories (with two supercharges) having tensor-valued degrees of freedom which are dominated by melon diagrams in the large $N$ limit. One motivation was to examine the interplay between supersymmetry and melonic dominance and potential implications for building toy models of holography. We find a definite tension between supersymmetry (with dynamical bosons) and melonic dominance in this class of systems. More specifically, our theories attain a low energy non-supersymmetric conformal fixed point. The origin of supersymmetry breaking lies in the need to regularize bosonic and fermionic degrees of freedom independently. We investigate various aspects of the low energy spectrum and also comment on related examples with different numbers of supercharges. Along the way we also derive some technical results for $SL(2,{\mathbb R})$ wavefunctions for fermionic excitations.