Hideki Kyono

Lax pairs on Yang-Baxter deformed backgrounds

A bstractWe explicitly derive Lax pairs for string theories on Yang-Baxter deformed backgrounds, 1) gravity duals for noncommutative gauge theories, 2) γ-deformations of S5, 3) Schrödinger spacetimes and 4) abelian twists of the global AdS5. Then we can find out a concise derivation of Lax pairs based on simple replacement rules. Furthermore, each of the above deformations can be reinterpreted as twisted boundary conditions with the undeformed background by using the rules. As another derivation, the Lax pair for gravity duals for noncommutative gauge theories is reproduced from the one for a q-deformed AdS5×S5 by taking a scaling limit.

Yang-Baxter sigma models and Lax pairs arising from κ-Poincare r-matrices

A bstractWe 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 dS4 and AdS4, 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.

Chaotic strings in a near Penrose limit of AdS 5 × T 1,1

A bstractWe study chaotic motions of a classical string in a near Penrose limit of AdS5 × T1,1. It is known that chaotic solutions appear on R ×T1,1, depending on initial conditions. It may be interesting to ask whether the chaos persists even in Penrose limits or not. In this paper, we show that sub-leading corrections in a Penrose limit provide an unstable separatrix, so that chaotic motions are generated as a consequence of collapsed KolmogorovArnold-Moser (KAM) tori. Our analysis is based on deriving a reduced system composed of two degrees of freedom by supposing a winding string ansatz. Then, we provide support for the existence of chaos by computing Poincaré sections. In comparison to the AdS5 ×T1,1 case, we argue that no chaos lives in a near Penrose limit of AdS5×S5, as expected from the classical integrability of the parent system.

Anatomy of Geodesic Witten Diagrams

A bstractWe 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.

Comments on 2D dilaton gravity system with a hyperbolic dilaton potential

Abstract We proceed to study a ( 1 + 1 )-dimensional dilaton gravity system with a hyperbolic dilaton potential. Introducing a couple of new variables leads to two copies of Liouville equations with two constraint conditions. In particular, in conformal gauge, the constraints can be expressed with Schwarzian derivatives. We revisit the vacuum solutions in light of the new variables and reveal its dipole-like structure. Then we present a time-dependent solution which describes formation of a black hole with a pulse. Finally, the black hole thermodynamics is considered by taking account of conformal matters from two points of view: 1) the Bekenstein–Hawking entropy and 2) the boundary stress tensor. The former result agrees with the latter one with a certain counter-term.

Lax pairs for deformed Minkowski spacetimes

A bstractWe proceed to study Yang-Baxter deformations of 4D Minkowski spacetime based on a conformal embedding. We first revisit a Melvin background and argue a Lax pair by adopting a simple replacement law invented in 1509.00173. This argument enables us to deduce a general expression of Lax pair. Then the anticipated Lax pair is shown to work for arbitrary classical r-matrices with Poincaré generators. As other examples, we present Lax pairs for pp-wave backgrounds, the Hashimoto-Sethi background, the Spradlin-Takayanagi-Volovich background.

Yang–Baxter invariance of the Nappi–Witten model

Abstract We study Yang–Baxter deformations of the Nappi–Witten model with a prescription invented by Delduc, Magro and Vicedo. The deformations are specified by skew-symmetric classical r -matrices satisfying (modified) classical Yang–Baxter equations. We show that the sigma-model metric is invariant under arbitrary deformations (while the coefficient of B -field is changed) by utilizing the most general classical r -matrix. Furthermore, the coefficient of B -field is determined to be the original value from the requirement that the one-loop β -function should vanish. After all, the Nappi–Witten model is the unique conformal theory within the class of the Yang–Baxter deformations preserving the conformal invariance.

Deformations of the Almheiri-Polchinski model

A bstractWe study deformations of the Almheiri-Polchinski (AP) model by employing the Yang-Baxter deformation technique. The general deformed AdS2 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.

Melnikov's method in String Theory

A bstractMelnikov’s method is an analytical way to show the existence of classical chaos generated by a Smale horseshoe. It is a powerful technique, though its applicability is somewhat limited. In this paper, we present a solution of type IIB supergravity to which Melnikov’s method is applicable. This is a brane-wave type deformation of the AdS5×S5 background. By employing two reduction ansätze, we study two types of coupled pendulum-oscillator systems. Then the Melnikov function is computed for each of the systems by following the standard way of Holmes and Marsden and the existence of chaos is shown analytically.

Towards spinning Mellin amplitudes

Abstract We construct the Mellin representation of four point conformal correlation function with external primary operators with arbitrary integer spacetime spins, and obtain a natural proposal for spinning Mellin amplitudes. By restricting to the exchange of symmetric traceless primaries, we generalize the Mellin transform for scalar case to introduce discrete Mellin variables for incorporating spin degrees of freedom. Based on the structures about spinning three and four point Witten diagrams, we also obtain a generalization of the Mack polynomial which can be regarded as a natural kinematical polynomial basis for computing spinning Mellin amplitudes using different choices of interaction vertices.