Conformality of $1/N$ corrections in SYK-like models
Stéphane Dartois, Harold Erbin, Swapnamay Mondal
TL;DR
This work investigates whether conformal invariance of the two-point function in SYK-like theories persists at next-to-leading order in the $1/N$ expansion. Using Schwinger–Dyson equations, ladder graph analysis, and a composite-field viewpoint, the authors analyze the colored SYK model with disorder and real/complex colored tensor variants, establishing that the NLO two-point function retains the same IR scaling as LO (dimension $\Delta = 1/q$ or $\Delta = 1/(D+1)$) up to explicit pseudo-Goldstone contributions. They find that, for colored SYK with disorder and for real/complex colored tensor models, conformality is preserved at NLO in the strong-coupling IR, while in the multi-orientable tensor model the NLO analysis does not decisively fix conformal behavior. The results have potential implications for the bulk AdS$_2$/CFT$_1$ dual, suggesting a suppression of quantum corrections at leading order, and point to future work on higher-point functions, NNLO, and refined composite-field methods to fully map the conformal structure.
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.