Towards a double-scaling limit for tensor models: probing sub-dominant orders

TL;DR

This paper investigates the next-to-leading order contributions in tensor models to understand the potential for a double-scaling limit, revealing key properties that suggest a non-trivial limit may exist.

Contribution

It analyzes NLO contributions in IID tensor models, providing initial insights and conjectures towards establishing a double-scaling limit in tensor models.

Findings

NLO series radius of convergence matches leading melonic sector

Susceptibility exponent at NLO is 3/2, indicating a departure from leading order behavior

Provides conjectures for a non-trivial double-scaling limit

Abstract

The definition of a double-scaling limit represents an important goal in the development of tensor models. We take the first steps towards this goal by extracting and analysing the next-to-leading order contributions, in the 1/N expansion, for the IID tensor models. We show that the radius of convergence of the NLO series coincides with that of the leading order melonic sector. Meanwhile, the value of the susceptibility exponent at NLO is 3/2, signaling a departure from the leading order behaviour. Both pieces of information provide clues for a non-trivial double-scaling limit, for which we put forward some precise conjecture.