Dynamics of tensor and SYK models
Date/Time: 17:00 18-Oct-2019
Abstract:
I review the combinatorics of models where the degrees of freedom are tensors of rank three or higher. For specially chosen interactions, the Feynman graph expansion is dominated by the so-called melonic graphs in the large N limit. I present the simplest tensor quantum mechanical model for Majorana fermions with a quartic Hamiltonian, which was introduced in my work with G. Tarnopolsky, and compare it with the Sachdev-Ye-Kitaev model. When two tensor or SYK models are coupled by a quartic interaction, a gap can open up for sufficiently large $N$ between two nearby lowest energy states and the rest of the spectrum. This suggests spontaneous breaking of a $Z_2$ symmetry. Analysis of the large-N Schwinger-Dyson equations shows that a symmetry-breaking operator indeed acquires an expectation value, demonstrating a pairing mechanism in melonic theories.
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Authors
Klebanov Igor
(Presenter)
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