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arXiv:2004.13744 · Corfu Summer Institute School and Workshops on Elementary Particle Physics and Gravity (CORFU)

The Tensor Track VI: Field Theory on Random Trees and SYK on Random Unicyclic Graphs

Nicolas Delporte, Vincent Rivasseau

Published Aug 18, 2020• 8 citations

arXiv HTML PDF

Abstract

We review the paper [arXiv:1905.12783] and discuss some comments about SYK on random unicycle.

DOI: 10.22323/1.376.0207

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The Sachdev-Ye-Kitaev (SYK) model is a model of

q

interacting fermions whose large N limit is dominated by melonic graphs. In this review we first present a diagrammatic proof of that result by direct, combinatorial analysis of its Feynman graphs. Gross and Rosenhaus have then proposed a generalization of the SYK model which involves fermions with different flavors. In terms of Feynman graphs, these flavors can be seen as reminiscent of the colors used in random tensor theory. Applying modern tools from random tensors to such a colored SYK model, all leading and next-to-leading orders diagrams of the 2-point and 4-point functions in the large

N

expansion can be identified. We then study the effect of non-Gaussian average over the random couplings in a complex, colored version of the SYK model. Using a Polchinski-like equation and random tensor Gaussian universality, we show that the effect of this non-Gaussian averaging leads to a modification of the variance of the Gaussian distribution of couplings at leading order in

N

. We then derive the form of the effective action to all orders.