We proceed to study Yang-Baxter deformations of the AdS 5 ×S 5 superstring with the classical Yang-Baxter equation. We make a general argument on the supercoset construction and present a formula to describe the dilaton in terms of classical rmatrices. The supercoset construction is explicitly performed for some classical rmatrices and the full backgrounds including the Ramond-Ramond (R-R) sector and dilaton are derived. Within the class of abelian r-matrices, the perfect agreement is shown for well-known examples including gravity duals of non-commutative gauge theories, γ-deformations of S 5 and Schrödinger spacetimes. It is remarkable that the supercoset construction works well, even if the resulting backgrounds are not maximally supersymmetric. In particular, three-parameter γ-deformations of S 5 and Schrödinger spacetimes do not preserve any supersymmetries. As for non-abelian r-matrices, we will focus upon a specific example. The resulting background does not satisfy the equation of motion of the Neveu-Schwarz-Neveu-Schwarz (NS-NS) two-form becauseThis coset enjoys the Z 4 -grading property and ensures classical integrability [9] (for a nice review, see [10]). The integrability plays an important role in checking the conjectured relation in AdS/CFT (for a comprehensive review, see [11]). By employing the Yang-Baxter deformation, Delduc, Magro and Vicedo constructed the classical action of a q-deformed AdS 5 ×S 5 superstring [12]. This deformation comes from the classical r-matrix of Drinfel'd-Jimbo type satisfying the mCYBE [13]. The string-frame metric and Neveu-Schwarz-Neveu-Schwarz (NS-NS) two-form were derived by Arutyunov, Borsato and Frolov [14]. Then they performed the supercoset construction and derived the remaining sector [15] (for earlier attempts, see [16, 17]). As a result, the full background does not satisfy the equations of motion of type IIB supergravity, although it is related to a complete solution [18] via T-dualities apart from the dilaton part. In particular, the dilaton cannot be separated so that the Ramond-Ramond (R-R) flux should satisfy the Bianchi identity. Recently, Arutyunov et al. proposed an exciting conjecture that type IIB supergravity itself would get deformed, for example, the definition of R-R field strength may be modified [19]. This "modified gravity conjecture" may be connected to our result presented here.One may also consider Yang-Baxter deformations of the AdS 5 ×S 5 superstring with classical r-matrices satisfying the homogeneous CYBE [20]. A strong advantage in this case is that partial deformations of AdS 5 ×S 5 are possible. In fact, for well-known backgrounds including gravity duals of noncommutative gauge theories [21,22], γ-deformations of S 5 [23,24],

Abstract:We revisit the so-called "Geodesic Witten Diagrams" (GWDs) [1], proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related "split representation" for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.

We study deformations of the Almheiri-Polchinski (AP) model by employing the Yang-Baxter deformation technique. The general deformed AdS 2 metric becomes a solution of a deformed AP model. In particular, the dilaton potential is deformed from a simple quadratic form to a hyperbolic function-type potential similarly to integrable deformations. A specific solution is a deformed black hole solution. Because the deformation makes the spacetime structure around the boundary change drastically and a new naked singularity appears, the holographic interpretation is far from trivial. The Hawking temperature is the same as the undeformed case but the Bekenstein-Hawking entropy is modified due to the deformation. This entropy can also be reproduced by evaluating the renormalized stress tensor with an appropriate counter-term on the regularized screen close to the singularity.

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We study Yang-Baxter sigma models with deformed 4D Minkowski spacetimes arising from classical r-matrices associated with κ-deformations of the Poincaré algebra. These classical κ-Poincaré r-matrices describe three kinds of deformations: 1) the standard deformation, 2) the tachyonic deformation, and 3) the light-cone deformation. For each deformation, the metric and two-form B-field are computed from the associated r-matrix. The first two deformations, related to the modified classical Yang-Baxter equation, lead to T-duals of dS 4 and AdS 4 , respectively. The third deformation, associated with the homogeneous classical Yang-Baxter equation, leads to a time-dependent pp-wave background. Finally, we construct a Lax pair for the generalized κ-Poincaré r-matrix that unifies the three kinds of deformations mentioned above as special cases.