The Non-melonic Sector of Tensor Models and Gravity

TL;DR

This paper explores the significance of non-melonic contributions in tensor models at large N, showing that they can dominate when the size of observables scales with N, which is crucial for recovering geometric structures and gravity.

Contribution

It demonstrates that non-melonic sectors become dominant in tensor models when observables grow with N, challenging the melonic dominance assumption for continuum gravity.

Findings

Non-melonic contributions can surpass melonic ones at large N.

Scaling of observables with N affects the dominance of tensor sectors.

Implications for the emergence of geometry and gravity from tensor models.

Abstract

The melonic sector has been proven to be dominant in tensor models at large N. This is true as long as the observables we consider, composites of 2n tensors, are small. That is, if n is much smaller than N. In this paper, I argue that, in order to recover geometries (and then gravity) in the continuum limit, n must grow like N. In that case, I provide examples where non-melonic contributions overcome the total sum in the computation of the expectation value of certain observables.