Emergence of Space-Time in the SYK Model

Kenta Suzuki

CPHT, Ecole Polytechnique

Fri, Mar. 08th 2019, 14:15-15:15

Salle Claude Itzykson, Bât. 774, Orme des Merisiers

The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical many-body system with random all-to-all interactions on fermionic N sites (N large). This model is shown to saturate the known maximal chaos bound of many-body system and then based on this observation it is conjectured to be dual to a quantum black hole in the sense of the AdS/CFT correspondence. In this talk, we start from reviewing basis aspects of the SYK model in the large N limit, which is systematically described by a single bi-local field. We show that a propagator of the bi-local field, which is understood as a four-point function of the original fermions, predicts an infinite spectrum of the dual AdS$_2$ theory, but it has a divergent contribution from the zero mode at the critical IR fixed point of the model. Next, we show that the spectrum of the four-point integration SYK model can be interpreted as that of a single scalar field coupled to gravity in 3 space-time dimension. The scalar field lives on AdS$_2$ * I, where I is a finite interval, and subject to a delta function potential at the center of the interval. Through Kaluza-Klein procedure on the third direction, this scalar generates the spectrum predicted by the SYK bi-local propagator at strong coupling. Finally, we consider the question of identifying the bulk space-time of the SYK model. Focusing on the signature of emergent space-time of the (Euclidean) model, we explain the need for non-local (Radon-type) transformations on external legs of n-point Green's functions. This results in a dual theory with Euclidean AdS signature with additional leg-factors. We speculate that these factors incorporate the coupling of additional bulk states similar to the discrete states of 2D string theory.

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