Abstract

The fascinating Sachdev-Ye-Kitaev (SYK) model describing a large number of randomly interacting Majorana fermions represents an ultimate example of the AdS/CFT correspondence in 1+1 space-time dimensions. As pointed out by Kitaev, both the SYK model and its gravity dual possess an emergent conformal symmetry which, however, is spontaneously broken in the infra-red. As such, the soft (or Goldstone) mode in the spectrum of the model emerges which is known to be described by the so-called 'Schwarzian' action. In my talk, after a general exposition to the SYK model, I will concentrate on its quantum deeply infra-red limit where conformal Goldstone fluctuations start to play a paramount role. I will demonstrate how the 'Schwarzian' action can be mapped onto a 'Liouvillian' quantum mechanics and study a long-time limit of 2- and 4-point correlation functions of Majoranas.