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.
Highlights
In a series of seminal conferences [1,2,3] Kitaev brought attention to the— so-called—Sachdev-Ye-Kitaev (SYK) model which displays a set of appealing features in the context of holography, for which a detailed account has been given in Ref. [4]
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 twopoint function in the strong-coupling regime, up to the contribution of the pseudo-Goldstone bosons due to the explicit breaking of the symmetry which are already seen in the leading-order four-point function
The problem we address in this paper is the opposite, i.e., is the conformal symmetry explicitly broken in the NLO in N for the leading order (LO) in the coupling constant? We consider this question in the models mentioned above: the colored1 SYK model with disorder, and the real, complex and multiorientable SYK tensor models
Summary
In a series of seminal conferences [1,2,3] Kitaev brought attention to the— so-called—Sachdev-Ye-Kitaev (SYK) model which displays a set of appealing features in the context of holography, for which a detailed account has been given in Ref. [4]. Since the full action breaks the symmetry explicitly but slightly, these are pseudo-Goldstone bosons, with their dynamics being described by the Schwarzian action The latter are responsible for the last property of the model: the Lyapunov exponent, which measures the chaos in the system, reaches the maximal bound proposed in Ref. The fact that one can access the strong-coupling regime offers an inestimable window on the quantum properties of black holes Another interesting property is its equivalence with random tensor fields theories in the large-N limit, as was pointed in Ref. We find that in the first three models the NLO twopoint function is compatible with conformal symmetry and should scale in the same way as the LO two-point function This means that in the infrared the dimension of the fermions is not modified by the first subleading correction in the large-N expansion. The Appendix describes how to perform a composite field analysis for the real colored tensor model
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