A sharp transition in quantum chaos and thermodynamics of mass deformed SYK model

We review our recent work [1] where we studied the chaotic property of the two coupled Sachdev-Ye-Kitaev systems exhibiting a Hawking-Page like phase transition. By computing the out-of-time-ordered correlator in the large NN limit by using the bilocal field formalism, we found that the chaos exponent of this model shows a discontinuous fall-off at the phase transition temperature. Hence in this model the Hawking-Page like transition is correlated with a transition in chaoticity, as expected from the relation between a black hole geometry and the chaotic behavior in the dual field theory.

Bilocal fields and gravity

We study a classical bilocal field theory perturbatively up to second-order. The chosen theory is the simplest which incorporates action-at-a-distance, while keeping nonlocal effects short-ranged. We show that the new degrees of freedom introduced by bilocality can be interpreted as gravitational degrees of freedom in the following sense: solutions of the bilocal system at linear and second-orders contain as a subset, gravitational perturbations (spacetime fluctuations) also to that order. In other words, gravity can be thought to originate in a bilocal field theory. We examine potential implications.

On 1/N diagrammatics in the SYK model beyond the conformal limit

In the present work we discuss aspects of the 1/N expansion in the SYK model, formulated in terms of the semiclassical expansion of the bilocal field path integral. We derive cutting rules, which are applicable for all planar vertices in the bilocal field diagrams. We show that these cutting rules lead to novel identities on higher-point correlators, which could be used to constrain their form beyond the solvable conformal limit. We also demonstrate how the cutting rules can simplify the computation of amplitudes on an example of the six-point function.

Stochastic Loop Equations

Stochastic quantization is applied to derivation of the equations for the Wilson loops and generating functionals of the Wilson loops in the N = ∞ limit. These equations are treated both in the coordinate and momentum representations. In the first case the connection of the suggested approach with the problem of random closed contours and supersymmetric quantum mechanics is established, and the equation for the Quenched Master Field Wilson loop is derived. The regularized version of one of the obtained equations is presented and applied to derivation of the equation for the bilocal field correlator. The momentum loop dynamics is also investigated.

SOLITONS IN A BILOCAL FIELD THEORY

We obtain a bilocal classical field theory as the large N limit of the chiral Gross-Neveu (or non-Abelian Thirring) model. Exact classical solutions that describe topological solitons are obtained. It is shown that their mass spectrum agrees with the large N limit of the spectrum of the chiral Gross-Neveu model.

A BILOCAL FIELD APPROACH TO THE LARGE N EXPANSION OF TWO-DIMENSIONAL (GAUGE) THEORIES

We consider a wide class of two-dimensional models as gauge theories, the Gross-Neveu model, O(N) and CPN−1-like models using a formalism based on the introduction of bilocal fields that permits us to perform easily the large N expansion of this set of models in a unified and general way. We mainly discuss the SU(N) gauge field theory minimally coupled to fermionic plus bosonic matter in the fundamental representation, and we obtain within the path integral approach exact equations for the particle spectrum, also in the presence of renormalizable polynomial potentials. Finally, we discuss the correspondence between this new approach and the one previously used in the context of the O(N) vector models.

THE MASTER FIELD OF QCD2 AND THE 't HOOFT EQUATION

We rewrite the action for QCD 2 in the light-cone gauge only in terms of a bilocal mesonic field. In this formalism the 1/N expansion can be done in a straightforward way by a saddle point technique that determines the master field to be identified with the vacuum expectation value of the bilocal field. Finally we show that the equation of motion for the fluctuations around the master field is identical with the 't Hooft meson equation.

TWO-DIMENSIONAL BARYONS IN THE LARGE-N LIMIT

We propose a bilocal field theory for mesons in two dimensions obtained as a kind of non-local bosonization of two-dimensional QCD. Its semiclassical expansion is equivalent to the 1/Nc expansion of QCD. Using an ansatz we reduce the classical equation of motion of this theory in the baryon number one sector to a relativistic Hartree equation and solve it numerically. This (non-topological) soliton is identified with the baryon.