Институт теоретической физики им. Л.Д. Ландау РАН
L.D. Landau Institute for Theoretical Physics RAS
International conference dedicated to the 100th anniversary of I. M. Khalatnikov
"Quantum Fluids, Quantum Field Theory, and Gravity"

October, 17-20, 2019 Chernogolovka, Russia

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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