# Conformality of $1/N$ corrections in SYK-like models

## TL;DR

This paper demonstrates that in SYK-like models, the next-to-leading order $1/N$ corrections do not break the conformal invariance of the 2-point function in the strong coupling limit, aside from known pseudo-Goldstone effects.

## Contribution

It shows that $1/N$ corrections in colored SYK and tensor models preserve conformal invariance of the 2-point function, extending understanding of their large $N$ behavior.

## Key findings

- Conformal invariance is preserved at next-to-leading order in $1/N$.
- Pseudo-Goldstone bosons account for explicit symmetry breaking effects.
- Comments on the composite field approach for correlation functions.

## Abstract

The Sachdev--Ye--Kitaev is a quantum mechanical model of $N$ Majorana fermions which displays a number of appealing features -- solvability in the strong coupling regime, near-conformal invariance and maximal chaos -- which make it a suitable model for black holes in the context of the AdS/CFT holography. In this paper, we show for the colored SYK model and several of its tensor model cousins that the next-to-leading order in the large $N$ expansion preserves the conformal invariance of the $2$-point function in the strong coupling regime, up to the contribution of the pseudo-Goldstone bosons due to the explicit breaking of the symmetry and which are already seen in the leading order $4$-point function. We also comment on the composite field approach for computing correlation functions in colored tensor models.