Holographic derivation of $q$ SYK spectrum with Yang-Baxter shift

In this Letter, based on the notion of gauge/gravity duality, we compute $q$ SYK spectra in the presence of Yang-Baxter (YB) deformations. The gravitational counterpart of this duality turns out to be the YB deformed Almheiri-Polchinski (AP) model embodied with hyperbolic potential for the dilaton. Following Kaluza-Klein reduction on $(Ad{S}_2{)}_{\eta }\times (S^1\mathrm{/}{Z}_2)$, we compute the deformed Green’s function that reproduces the original $q$ SYK spectrum in the limit of vanishing deformations.