Abstract
In this paper, based on the notion of SYK/AdS duality we explore the effects of Yang-Baxter (YB) deformations on the SYK spectrum at strong coupling. In the first part of our analysis, we explore the consequences of YB deformations through the Kaluza-Klein (KK) reduction on (AdS2)η × (S1)/Z2. It turns out that the YB effects (on the SYK spectrum) starts showing off at quadratic order in 1/J expansion. For the rest of the analysis, we provide an interpretation for the YB deformations in terms of bi-local/collective field excitations of the SYK model. Using large N techniques, we evaluate the effective action upto quadratic order in the fluctuations and estimate 1/J2 corrections to the correlation function at strong coupling.
Highlights
Understanding the dual gravitational counterpart [28]–[35] corresponding to the SYK model had always been challenging until very recently [36]–[38]
The motivation behind our analysis strictly follows from holography where we start with the deformed AdS2 version of the theory in the bulk [39] and lift it to three dimensions in order to compute the KK spectrum associated with the scalar field excitations in the dual gravitational counterpart
Our analysis reveals that the holographic correspondence between the SYK model and its dual gravitational counterpart brings into a non trivial 1/J2 corrections to the spectrum of the SYK model which has its origin in the YB deformations associated with the (AdS2)η × (S1)/Z2 theory in (2 + 1) D
Summary
The primary motivation behind introducing the Yang-Baxter (YB) deformations (associated with non-linear σ-models, e.g; the Principal Chiral Model (PCM)) was the observation that the later is equivalent to a two-dimensional field theory (defined on some compact manifold M) embodied with a rank 2 symmetric tensor (metric) field (γαβ) as well as an. These YB σ-models are characterized by some R-linear operators [44,45,46,47] and seem to posses a left-symmetry together with the Poisson-Lie symmetry with respect to the right action of the group on itself These symmetries of the model could be associated with certain types of dualities embedded in its structure.. The motivation behind introducing the YB deformations in the context of string sigma models stems from the fact that they play crucial role towards a profound understanding of the underlying dynamics in AdS/CFT correspondence. It eventually includes a broader classes of stringy geometries [48,49,50,51] within the unified framework of gauge/string duality. The purpose of the present analysis is to fill up this gap and provide a systematic realization of the dual gauge theory at strong coupling
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