Understanding the dual gravitational counterpart [28]–[35] corresponding to the SYK
model had always been challenging until very recently [36]–[38]. In [36], the authors provide
a very solid evidence in favour of the dual 3D gravitational counterpart corresponding to
the zero temperature version of the model where they explore the Kaluza-Klein (KK) tower
associated with the scalar field excitations on AdS
2
× (S
1
)/Z
2
. In the strict IR (|Jt| 1)
limit, the metric along the compact third direction becomes constant, whereas on the other
hand, away from the fixed point it acquires non trivial dependence on the AdS
2
coordinates
through the dilaton profile. In their analysis [36], the authors explore the 1/J corrections to
the zero modes of the theory and compute the strong coupling corrections to the propagator
that precisely matches to that with the earlier results in [8].
The purpose of the present paper is to explore and understand this duality conjecture
in the presence of so called Yang-Baxter (YB) deformations [39]–[41] and also to understand
its possible consequences on the corresponding bi-local excitations [13]–[14] associated with
the SYK model at strong coupling. The motivation behind our analysis strictly follows from
holography where we start with the deformed AdS
2
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/J
2
corrections to the spectrum of the SYK model which has
its origin in the YB deformations associated with the (AdS
2
)
η
×(S
1
)/Z
2
theory in (2 + 1)
D. For the rest of our analysis, we search for an interpretation of such deformations in
terms of collective field excitations [42, 43] associated with the SYK model. Looking
at the holographic side of the duality, we propose a possible YB scaling of the collective
excitations within the SYK model and compute the effective action at quadratic order in
the fluctuations (around IR critical point) and thereby the corresponding propagator at
strong coupling (|Jt| 1). Our analysis reveals that the effective action receives non trivial
1/J
2
corrections that has remarkable structural similarity to that with the corresponding
quadratic action associated with scalar field excitations computed on the dual gravitational
counterpart of the theory.
The organisation of the paper is as follows: in section 2, we briefly review the YB
deformations and its implications on the Almheiri-Polchinski (AP) model [39]–[41]. In
section 3, we compute the zero modes associated with the spectrum and estimate the 1/J
2
corrections to it. In section 4, we provide a possible interpretation of the YB effects on the
collective excitations within the SYK model. Finally, we conclude in section 5.
2 YB deformations and string theory
2.1 Basics
The primary motivation behind introducing the Yang-Baxter (YB) deformations (associ-
ated 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 (γ
αβ
) as well as an
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