Kazuhiro Sakai

Keio University, Edo, Tōkyō, Japan

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Publications (10)54.08 Total impact

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    ABSTRACT: We study gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills theory at strong coupling by calculating the area of the minimal surfaces in AdS_3 based on the associated thermodynamic Bethe ansatz system. The remainder function of the amplitudes is computed by evaluating the free energy, the T- and Y-functions of the homogeneous sine-Gordon model. Using conformal field theory (CFT) perturbation, we examine the mass corrections to the free energy around the CFT point corresponding to the regular polygonal Wilson loop. Based on the equivalence between the T-functions and the g-functions, which measure the boundary entropy, we calculate corrections to the T- and Y-functions as well as express them at the CFT point by the modular S-matrix. We evaluate the remainder function around the CFT point for 8 and 10-point amplitudes explicitly and compare these analytic expressions with the 2-loop formulas. The two rescaled remainder functions show very similar power series structures.
    Journal of High Energy Physics 02/2011; 2011(4). · 5.62 Impact Factor
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    ABSTRACT: We study six-point gluon scattering amplitudes in N = 4 \mathcal{N} = 4 super Yang-Mills theory at strong coupling by investigating the thermodynamic Bethe ansatz equations of the underlying \mathbbZ4 {\mathbb{Z}_4} -symmetric integrable model both analytically and numerically. By the conformal field theory (CFT) perturbation, we compute the free energy part of the remainder function with generic chemical potential near the CFT/small mass limit. Combining this with the expansion of the Y-functions, we obtain the remainder function near the small mass limit up to a function of the chemical potential, which can be evaluated numerically. We also find the leading corrections to the remainder function near the large mass limit. We confirm that these results are in good agreement with numerical computations. KeywordsIntegrable Equations in Physics–AdS-CFT Correspondence–Bethe Ansatz
    Journal of High Energy Physics 05/2010; 2010(9):1-26. · 5.62 Impact Factor
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    ABSTRACT: We study classical open string solutions with a null polygonal boundary in AdS_3 in relation to gluon scattering amplitudes in N=4 super Yang-Mills at strong coupling. We derive in full detail the set of integral equations governing the decagonal and the dodecagonal solutions and identify them with the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon models. By evaluating the free energy in the conformal limit we compute the central charges, from which we observe general correspondence between the polygonal solutions in AdS_n and generalized parafermions. Comment: 25 pages, 4 figures, v2: a figure and references added, minor corrections, v3: references added, minor corrections, to appear in JHEP
    Journal of High Energy Physics 02/2010; · 5.62 Impact Factor
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    Kazuhiro Sakai, Yuji Satoh
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    ABSTRACT: We construct constant mean curvature surfaces of the general finite-gap type in AdS 3. The special case with zero mean curvature gives minimal surfaces relevant for the study of Wilson loops and gluon scattering amplitudes in N = 4 \mathcal{N} = 4 super Yang-Mills. We also analyze properties of the finite-gap solutions including asymptotic behavior and the degenerate (soliton) limit, and discuss possible solutions with null boundaries. KeywordsIntegrable Equations in Physics-AdS-CFT Correspondence-Sigma Models
    Journal of High Energy Physics 01/2010; 2010(3):1-18. · 5.62 Impact Factor
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    ABSTRACT: We study six-point gluon scattering amplitudes in $$ \mathcal{N} = 4 $$ super Yang-Mills theory at strong coupling by investigating the thermodynamic Bethe ansatz equations of the underlying $$ {\mathbb{Z}_4} $$-symmetric integrable model both analytically and numerically. By the conformal field theory (CFT) perturbation, we compute the free energy part of the remainder function with generic chemical potential near the CFT/small mass limit. Combining this with the expansion of the Y-functions, we obtain the remainder function near the small mass limit up to a function of the chemical potential, which can be evaluated numerically. We also find the leading corrections to the remainder function near the large mass limit. We confirm that these results are in good agreement with numerical computations.
    Journal of High Energy Physics 01/2010; · 5.62 Impact Factor
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    Kazuhiro Sakai, Yuji Satoh
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    ABSTRACT: We systematically search for classical open string solutions in AdS3 within the general class expressed by elliptic functions (i.e., the genus-one finite-gap solutions). By explicitly solving the reality and Virasoro conditions, we give a classification of the allowed solutions. When the elliptic modulus degenerates, we find a class of solutions with six null boundaries, among which two pairs are collinear. By adding the S1 sector, we also find four-cusp solutions with null boundaries expressed by the elliptic functions.
    Journal of High Energy Physics 09/2009; 2009(10):001. · 5.62 Impact Factor
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    Kazuhiro Sakai, Yuji Satoh
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    ABSTRACT: We consider entanglement through permeable interfaces in the c=1 (1+1)-dimensional conformal field theory. We compute the partition functions with the interfaces inserted. By the replica trick, the entanglement entropy is obtained analytically. The entropy scales logarithmically with respect to the size of the system, similarly to the universal scaling of the ordinary entanglement entropy in (1+1)-dimensional conformal field theory. Its coefficient, however, is not constant but controlled by the permeability, the dependence on which is expressed through the dilogarithm function. The sub-leading term of the entropy counts the winding numbers, showing an analogy to the topological entanglement entropy which characterizes the topological order in (2+1)-dimensional systems.
    Journal of High Energy Physics 10/2008; · 5.62 Impact Factor
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    Kazuhiro Sakai, Yuji Satoh
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    ABSTRACT: We develop the derivation we proposed in hep-th/0703177 of the dressing phase of the S-matrix in the AdS/CFT correspondence in the framework of the underlying bare integrable model. We elaborate the configuration of the Bethe roots describing the physical vacuum, which consists of a long Bethe string stretched along the imaginary axis and stacks distributed along the real axis. We determine the distribution of all Bethe roots in the thermodynamic limit. We then directly compute the scattering phase of the fundamental excitations over the physical vacuum and reproduce the BHL/BES dressing phase. Comment: 23 pages, no figures; v2: references and minor clarifications added, version to be published in JHEP
    Journal of High Energy Physics 09/2007; · 5.62 Impact Factor
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    Kazuhiro Sakai, Yuji Satoh
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    ABSTRACT: We derive the phase factor proposed by Beisert, Eden and Staudacher for the S-matrix of planar N=4 super-Yang–Mills, from the all-loop Bethe ansatz equations without the dressing factor. We identify a configuration of the Bethe roots, from which the closed integral formula of the phase factor is reproduced in the thermodynamic limit. This suggests that our configuration describes the “physical vacuum” in the sense that the dressing phase is nothing but the effective phase for the scattering of fundamental excitations above this vacuum, providing an interesting clue to the physical origin of the dressing phase.
    Physics Letters B 04/2007; · 4.57 Impact Factor
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    Kazuhiro Sakai, Yuji Satoh
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    ABSTRACT: We study the scaling law of the energy spectrum of classical strings on AdS5×S5, in particular, in the SL(2) sector for large S (AdS spin) and fixed J (S1⊂S5 spin). For any finite gap solution, we identify the limit in which the energy exhibits the logarithmic scaling in S, characteristic to the anomalous dimension of low-twist gauge theory operators. Our result therefore shows that the logS scaling, first observed by Gubser, Klebanov and Polyakov for the folded string, is universal also on the string side, suggesting another interesting window to explore the AdS/CFT correspondence as in the BMN/Frolov–Tseytlin limit.
    Physics Letters B 02/2007; 645:293-298. · 4.57 Impact Factor