Abstract
It has recently been demonstrated that the large N limit of a model of fermions charged under the global/gauge symmetry group O(N)q−1 agrees with the large N limit of the SYK model. In these notes we investigate aspects of the dynamics of the O(N)q−1 theories that differ from their SYK counterparts. We argue that the spectrum of fluctuations about the finite temperature saddle point in these theories has left(q-1right)frac{N^2}{2} new light modes in addition to the light Schwarzian mode that exists even in the SYK model, suggesting that the bulk dual description of theories differ significantly if they both exist. We also study the thermal partition function of a mass deformed version of the SYK model. At large mass we show that the effective entropy of this theory grows with energy like E ln E (i.e. faster than Hagedorn) up to energies of order N2. The canonical partition function of the model displays a deconfinement or Hawking Page type phase transition at temperatures of order 1/ln N. We derive these results in the large mass limit but argue that they are qualitatively robust to small corrections in J/m.
Highlights
It has recently been demonstrated that the dynamically rich Sachdev-Ye-Kitaev model — a quantum mechanical model of fermions interacting with random potentials — is solvable at large N [1,2,3]
It has recently been demonstrated that the large N limit of a model of fermions charged under the global/gauge symmetry group O(N )q−1 agrees with the large N limit of the SYK model
These facts have motivated the suggestion that the SYK model is the boundary dual of a highly curved bulk gravitational theory whose finite temperature behaviour is dominated by a black hole saddle point
Summary
It has recently been demonstrated that the dynamically rich Sachdev-Ye-Kitaev model — a quantum mechanical model of fermions interacting with random potentials — is solvable at large N [1,2,3]. The connection between the quantum mechanical theories (1.1) and the SYK model itself is the following; it has been demonstrated (subject to certain caveats) that sum over Feynman graphs of the theory (1.1) coincides with the sum over Feynman graphs of the SYK model at at leading order at large N (see [16] for the argument in a very similar model), even though these two sums differ at finite values of N (see e.g. the recent paper [27] and references therein) It follows that the quantum mechanical models (1.1) are exactly as solvable as the SYK model at large N ; they inherit much of the dynamical richness of the SYK model. In other words the models (1.1) are solvable at large N , are unitary and are potentially boundary duals of (highly curved) black hole physics Motivated by these considerations, in this note we study the effective theory that governs the long time dynamics of the model (1.1) at finite temperature. In the rest of this introduction we will explain and describe our principal observations and results
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
