arXiv subjects

Kentaroh Yoshida

Publications and source records attributed to Kentaroh Yoshida.

At least 55 records · Page 3Linked to original sources

arXiv2017

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

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.

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arXiv2017

Generalized gravity from modified DFT

Recently, generalized equations of type IIB supergravity have been derived from the requirement of classical kappa-symmetry of type IIB superstring theory in the Green-Schwarz formulation. These equations are covariant under generalized T-duality transformations and hence one may expect a formulation similar to double field theory (DFT). In this paper, we consider a modification of the DFT equations of motion by relaxing a condition for the generalized covariant derivative with an extra generalized vector. In this modified double field theory (mDFT), we show that the flatness condition of the modified generalized Ricci tensor leads to the NS-NS part of the generalized equations of type IIB supergravity. In particular, the extra vector fields appearing in the generalized equations correspond to the extra generalized vector in mDFT. We also discuss duality symmetries and a modification of the string charge in mDFT.

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arXiv2017

Deformations of the Almheiri-Polchinski model

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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arXiv2016

Chaos in chiral condensates in gauge theories

Assigning a chaos index for dynamics of generic quantum field theories is a challenging problem, because the notion of Lyapunov exponent, which is useful for singling out chaotic behaviors, works only in classical systems. We address the issue by using the AdS/CFT correspondence, as the large $N_c$ limit provides a classicalization (other than the standard $\hbar \to 0$) while keeping nontrivial quantum condensation. We demonstrate the chaos in the dynamics of quantum gauge theories: Time evolution of homogeneous quark condensates $\langle \bar{q}q\rangle$ and $\langle \bar{q} γ_5 q\rangle$ in an ${\cal N}=2$ supersymmetric QCD with the $SU(N_c)$ gauge group at large $N_c$ and at large 't Hooft coupling $λ\equiv N_c g_{\rm YM}^2$ exhibits a positive Lyapunov exponent. The chaos dominates the phase space for energy density $E \gtrsim (6\times 10^2)\times m_q^4(N_c/λ^2) $ where $m_q$ is the quark mass. We evaluate the largest Lyapunov exponent as a function of $(N_c,λ,E)$ and find that the ${\cal N}=2$ supersymmetric QCD is more chaotic for smaller $N_c$.

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arXiv2016

The fate of chaotic strings in a confining geometry

We study chaotic motion of classical closed strings in the five-dimensional Anti-de Sitter (AdS) soliton spacetime. We first revisit classical chaos using a cohomogeneity-1 string ansatz. We then consider turbulent behaviors of the classical strings when the spatial dependence of the string world-sheet is included. Sensitivity to initial conditions in chaotic systems suggests that the string under chaos tends to stretch in the AdS soliton spacetime in a Lyapunov timescale. In this process, the orbital angular momentum transfers to internal spin due to the turbulence on the string. It follows that the string stays around the tip of the AdS soliton with a jumbled profile. We evaluate the spectra of conserved quantities and discuss their universal power-law scalings in the turbulent behaviors.

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arXiv2016

Supercoset construction of Yang-Baxter deformed AdS$_5\times$S$^5$ backgrounds

We proceed to study Yang-Baxter deformations of the AdS$_5\times$S$^5$ superstring with the classical Yang-Baxter equation. We make a general argument on the supercoset construction and present the master formula to describe the dilaton in terms of classical $r$-matrices. The supercoset construction is explicitly performed for some classical $r$-matrices 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 would be 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 because the R-R three-form is not closed.

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arXiv2016

Melnikov's method in String Theory

Melnikov'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 AdS$_5\times$S$^5$ 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.

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arXiv2016

Generalized type IIB supergravity equations and non-Abelian classical r-matrices

We study Yang-Baxter deformations of the $AdS_5 \times S^5$ superstring with non-Abelian classical $r$-matrices which satisfy the homogeneous classical Yang-Baxter equation (CYBE). By performing a supercoset construction, we can get deformed $AdS_5 \times S^5$ backgrounds. While this is a new area of research, the current understanding is that Abelian classical $r$-matrices give rise to solutions of type IIB supergravity, while non-Abelian classical $r$-matrices lead to solutions of the generalized supergravity equations. We examine here some examples of non-Abelian classical r-matrices and derive the associated backgrounds explicitly. All of the resulting backgrounds satisfy the generalized equations. For some of them, we derive "T-dualized" backgrounds by adding a linear coordinate dependence to the dilaton and show that these satisfy the usual type IIB supergravity equations. Remarkably, some of the "T-dualized" backgrounds are locally identical to undeformed $AdS_5 \times S^5$ after an appropriate coordinate transformation, but this seems not to be generally the case.

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arXiv2016

Generalized quark-antiquark potentials from a $q$-deformed AdS$_5 \times $S$^5$ background

We study minimal surfaces with a single cusp in a $q$-deformed AdS$_5\times$S$^5$ background. The cusp is composed of two half-lines with an arbitrary angle and is realized on a surface specified in the deformed AdS$_5$. The classical string solutions attached to this cusp are regarded as a generalization of configurations studied by Drukker and Forini in the undeformed case. By taking an antiparallel-lines limit, a quark-antiquark potential for the $q$-deformed case is derived with a certain subtraction scheme. The resulting potential becomes linear at short distances with a finite deformation parameter. In particular, the linear behavior for the gravity dual of noncommutative gauge theories can be reproduced as a special scaling limit. Finally we study the near straight-line limit of the potential.

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arXiv2016

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

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.

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arXiv2016

Yang-Baxter invariance of the Nappi-Witten model

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.

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arXiv2015

Lax pairs for deformed Minkowski spacetimes

We 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 Poincaé generators. As other examples, we present Lax pairs for pp-wave backgrounds, the Hashimoto-Sethi background, the Spradlin-Takayanagi-Volovich background.

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arXiv2015

Lax pairs on Yang-Baxter deformed backgrounds

We explicitly derive Lax pairs for string theories on Yang-Baxter deformed backgrounds, 1) gravity duals for noncommutative gauge theories, 2) $γ$-deformations of S$^5$, 3) Schrödinger spacetimes and 4) abelian twists of the global AdS$_5$\,. 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 a twisted periodic 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 AdS$_5\times$S$^5$ by taking a scaling limit.

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arXiv2015

Towards the gravity/CYBE correspondence beyond integrability -- Yang-Baxter deformations of $T^{1,1}$

Yang-Baxter sigma models, proposed by Klimcik and Delduc-Magro-Vicedo, have been recognized as a powerful framework for studying integrable deformations of two-dimensional non-linear sigma models. In this short article, as an important generalization, we review a non-integrable sigma model in the Yang-Baxter sigma model approach based on [arXiv:1406.2249]. In particular, we discuss a family of deformations of the 5D Sasaki-Einstein manifold $T^{1,1}$, instead of the standard deformations of the $5$-sphere S$^5$. For this purpose, we first describe a novel construction of $T^{1,1}$ as a supercoset, and provide a physical interpretation of this construction from viewpoint of the dual Klebanov-Witten field theory. Secondly, we consider a $3$-parameter deformation of $T^{1,1}$ by using classical $r$-matrices satisfying the classical Yang--Baxter equation (CYBE). The resulting metric and NS-NS two-form completely agree with the ones previously obtained via TsT (T-dual -- shift -- T-dual) transformations, and contain the Lunin-Maldacena background as a special case. Our result indicates that what we refer to as the gravity/CYBE(Classical Yang-Baxter Equation) correspondence can be extended beyond integrable cosets.

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arXiv2015

Chaotic strings in a near Penrose limit of AdS$_5\times T^{1,1}$

We study chaotic motions of a classical string in a near Penrose limit of AdS$_5\times T^{1,1}$. It is known that chaotic solutions appear on $R\times T^{1,1}$, 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 Kolmogorov-Arnold-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 Poincare sections. In comparison to the AdS$_5\times T^{1,1}$ case, we argue that no chaos lives in a near Penrose limit of AdS$_5\times$S$^5$, as expected from the classical integrability of the parent system.

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arXiv2015

Chaos in the BMN matrix model

We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ansätze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincaré sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.

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arXiv2015

Yang-Baxter sigma models based on the CYBE

It is known that Yang-Baxter sigma models provide a systematic way to study integrable deformations of both principal chiral models and symmetric coset sigma models. In the original proposal and its subsequent development, the deformations have been characterized by classical $r$-matrices satisfying the modified classical Yang-Baxter equation (mCYBE). In this article, we propose the Yang-Baxter sigma models based on the classical Yang-Baxter equations (CYBE) rather than the mCYBE. This generalization enables us to utilize various kinds of solutions of the CYBE to classify integrable deformations. In particular, it is straightforward to realize partial deformations of the target space without loss of the integrability of the parent theory.

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arXiv2015

Yang-Baxter deformations of Minkowski spacetime

We study Yang-Baxter deformations of 4D Minkowski spacetime. The Yang-Baxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation. It has been extended to coset curved spaces and models based on the usual classical Yang-Baxter equation. On the other hand, for flat space, there is the obvious problem that the standard bilinear form degenerates if we employ the familiar coset Poincaré group/Lorentz group. Instead we consider a slice of AdS$_5$ by embedding the 4D Poincaré group into the 4D conformal group $SO(2,4)$. With this procedure we obtain metrics and $B$-fields as Yang-Baxter deformations which correspond to well-known configurations such as T-duals of Melvin backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, the T-dual of Grant space, pp-waves, and T-duals of dS$_4$ and AdS$_4$. Finally we consider a deformation with a classical $r$-matrix of Drinfeld-Jimbo type and explicitly derive the associated metric and $B$-field which we conjecture to correspond to a new integrable system.

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