Ryuichi Nakayama |

Faculty of Science Physics Quantum Physics |

Associate Professor |

Last Updated :2020/09/10

- 1989 - 1993 文部省高エネルギー物理学研究所 助手
- 1989 - 1993 Research Assistant,
- 1988 - 1988 イタリア・トリエステ・高等研究所,研究員
- 1988 - 1988 Postdoctoral Fellow, SISSA(Trieste, Italy)
- 1987 - 1988 デンマーク.北欧原子物理研究所,研究員
- 1987 - 1988 Postdoctoral Fellow, NORDITA (Denmark)
- 1985 - 1987 デンマーク.ニールスボーア研究所,研究員
- 1985 - 1987 Postdoctoral Fellow,
- 1984 - 1985 文部省高エネルギー物理学研究所・日本学術振興会 奨励研究員
- 1984 - 1985 JSPS Fellow,
- National Laboratory for High Energy Physics
- Niels Bohr Institute(Denmark)
- National Laboratory for High Energy Physics

- - 1984 The University of Tokyo
- - 1984 The University of Tokyo Graduate School of Science Physics
- - 1979 The University of Tokyo Faculty of Science
- - 1979 The University of Tokyo Faculty of Science Department of Physics

- Ryuichi NAKAYAMA, Kenji Shiohara, Tomotaka SuzukiNuclear Physics B940 393 - 426 2019/03 [Refereed][Not invited]
- Ryuichi Nakayama, Tomotaka SuzukiInternational Journal of Modern Physics A 33 (12) 1850061-1 - 1850061-23 0217-751X 2018/04/30 [Refereed][Not invited]

We construct a localized state of a scalar field in 3D spin-3 gravity. 3D spin-3 gravity is thought to be holographically dual to W3-extended CFT on a boundary at infinity. It is known that while W3 algebra is a nonlinear algebra, in the limit of large central charge c a linear finite-dimensional subalgebra generated by Wn (n = 0,±1,±2) and Ln (n = 0,±1) is singled out. The localized state is constructed in terms of these generators. To write down an equation of motion for a scalar field which is satisfied by this localized state, it is necessary to introduce new variables for an internal space α±, β±, γ, in addition to ordinary coordinates x± and y. The higher-dimensional space, which combines the bulk space-Time with the "internal space," which is an analog of superspace in supersymmetric theory, is introduced. The "physical bulk space-Time" is a 3D hypersurface with constant α±, β± and γ embedded in this space. We will work in Poincaré coordinates of AdS space and consider W-quasi-primary operators h(x+) with a conformal weight h in the boundary and study two and three point functions of W-quasi-primary operators transformed as eix+L-1heβ+W-1hh(0)e-β+W-1he-ix+L-1h. Here, Lnh and Wnh are sl(3,R) generators in the hyperbolic basis for Poincaré coordinates. It is shown that in the β+ ∞ limit, the conformal weight changes to a new value h′ = h/2. This may be regarded as a Renormalization Group (RG) flow. It is argued that this RG flow will be triggered by terms S β+W-1h + β-W-1h added to the action. - Ryuichi Nakayama, Tomotaka SuzukiPROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS 2017 (8) 083B06 2050-3911 2017/08 [Refereed][Not invited]

We consider the Almheiri-Polchinski model of the AdS(2) back-reaction coupled with a Liouville field, which is necessary for quantum consistency. In this model, the Liouville field is determined classically by a bulk conformal transformation. The boundary time is also reparametrized by this transformation. It is shown that the on-shell action on the boundary for the gravity sector is given by a bulk integral containing the Liouville field. This integral stems from Weyl anomaly and is SL(2,R) invariant. A prescription is given for computing correlation functions of the operators dual to massless scalars. The generating function of the correlation functions of these operators is given by a sum of matter action and the bulk integral containing the Liouville field. The latter integral leads to extra contributions to n(>= 6) point functions. - Ippei Fujisawa, Ryuichi NAKAYAMAProg. Theor. Exp. Phys. 2016 (7) 3 2050-3911 2016 [Refereed][Not invited]
- Ippei Fujisawa, Ryuichi NakayamaPHYSICAL REVIEW D 91 (12) 126005 1550-7998 2015/06 [Refereed][Not invited]

Surface-charge algebra associated with Bondi-Metzner-Sachs (BMS4) symmetry on the null infinity of asymptotically flat spacetime is studied via a Hamiltonian framework. A coordinate system, where boundaries of constant-time hypersurfaces cross the null infinity, is adopted. The equation itself, which determines the variation of the surface charges, turns out the same as that previously obtained via the covariant framework by Barnich and Troessaert and is nonintegrable for general radiation field C-AB. However, if C-AB is independent of retarded time u, the variation equation is integrable, and the conserved surface charges generate BMS4 algebra without central extension. - Ippei Fujisawa, Ryuichi NakayamaCLASSICAL AND QUANTUM GRAVITY 31 (1) 015003 0264-9381 2014/01 [Refereed][Not invited]

The action integral for a matter system composed of 0- and 2-forms, C and B-mu nu, topologically coupled to 3D spin-3 gravity is considered first in the frame-like formalism. The field C satisfies an equation of motion, partial derivative(mu) C+A(mu) C-C (A) over bar (mu) = 0, where A(mu) and (A) over bar (mu) are the Chern-Simons gauge fields. With a suitable gauge fixing of a new local symmetry and diffeomorphism, only one component of B-mu nu, say B-phi r, remains non-vanishing and satisfies partial derivative(mu) B-phi r+(A) over bar (mu) B-phi r-B-phi r A(mu) = 0. These equations are the same as those for 3D (free) Vasiliev scalars, C and (C) over tilde. The spin connection is eliminated by solving the equation of motion for the total action, and it is shown that in the resulting metric-like formalism, (BC) 2 interaction terms are induced because of the torsion. The world-volume components of the matter field, C-0, C-mu and C-(mu nu), are introduced by contracting the local-frame index of C with those of the inverse vielbeins, E-a(mu) and E-a((mu nu)), which were defined by the present authors in (2013 Class. Quantum Grav. 30 035003). 3D higher spin gravity theory contains various metric-like fields. These metric-like fields, as well as the new connections and the generalized curvature tensors, introduced in the above mentioned paper, are explicitly expressed in terms of the metric g(mu nu) and the spin-3 field phi(mu nu lambda) by means of the phi-expansion. The action integral for the pure spin-3 gravity in the metric-like formalism up to O(phi(2)), obtained before in the literature, is re-derived. Then the matter action is re-expressed in terms of g(mu nu), f(mu nu rho) and the covariant derivatives for spin-3 geometry. Spin-3 gauge transformation is extended to the matter fields. It is also found that the action of the matter-coupled theory in the metric-like formalism has larger symmetry than that of the pure spin-3 gravity. The matter-coupled theory in the metric-like formalism is invariant under the ordinary diffeomorphisms, because the vielbein and the spin connection are covariant vectors of diffeomorphisms. They are also gauge fields for the local translation. In the pure spin-3 gravity this symmetry provides the ordinary diffeomorphism and the spin-3 transformation in the metric-like formalism. When the matter is coupled, the local translation yields a new symmetry in the metric-like formalism, which does not contain diffeomorphism. - Ippei Fujisawa, Ryuichi NakayamaClassical and Quantum Gravity 30 (3) 035003 0264-9381 2013/02/07 [Refereed][Not invited]

A second-order formalism for the theory of 3D spin-3 gravity is considered. Such a formalism is obtained by solving the torsion-free condition for the spin connection ωa μ, and substituting the result into the action integral. In the first-order formalism of the spin-3 gravity defined in terms of SL(3, R) × SL(3, R) Chern-Simons (CS) theory, however, the generalized torsion-free condition cannot be easily solved for the spin connection, because the vielbein ea μ itself is not invertible. To circumvent this problem, extra vielbein-like fields e a(μν) are introduced as a functional of ea μ. New sets of affine-like connections ΓN μM are defined in terms of the metric-like fields, and a generalization of the Riemann curvature tensor is also presented. In terms of this generalized Riemann tensor the action integral in the second-order formalism is expressed. The transformation rules of the metric and the spin-3 gauge field under the generalized diffeomorphims are obtained explicitly. As in Einstein gravity, the new affine-like connections are related to the spin connection by a certain gauge transformation and a gravitational CS term expressed in terms of the new connections is also presented. © 2013 IOP Publishing Ltd. - Ryuichi NakayamaPROGRESS OF THEORETICAL PHYSICS 127 (3) 393 - 408 0033-068X 2012/03 [Refereed][Not invited]

A simple conformal quantum mechanics model of a d-component variable is proposed, which exactly reproduces the retarded Green functions and conformal weights of conformally coupled scalar fields in de Sitter spacetime seen by a static patch observer. It is found that the action integral of this model is automatically expressed by a complex integral over the time variable t along a closed contour in a way that is typical to the Schwinger-Keldysh formalism of a thermofield theory. Hence, this model is at finite temperature. The case of conformally coupled scalar fields in 3D Schwarzschild de Sitter space is also considered, and then a large N matrix model is obtained. - Ryuichi NakayamaPHYSICS LETTERS B 638 (2-3) 283 - 287 0370-2693 2006/07 [Refereed][Not invited]

It will be shown that the defining relations for fuzzy torus and deformed (squashed) sphere proposed by [J. Amlind, M. Bordemann, L. Hofer, J. Hoppe, H. Shimada, hep-th/0602290] (ABHHS) can be rewritten as a new algebra which contains q-deformed commutators. The quantum parameter q (vertical bar q vertical bar = 1) is a function of h. It is shown that the q -> 1 limit of the algebra with the parameter mu < 0 describes fuzzy S-2 and that the squashed S2 with q :0 1 and It < 0 can be regarded as a new kind of quantum S2. Throughout the Letter the value of the invariant of the algebra, which defines the constraint for the surfaces, is not restricted to be 1. This allows the parameter q to be treated as independent of N (the dimension of the representation) and A. It was shown by ABHHS that there are two types of representations for the algebra, "string solution" and "loop solution". The "loop solution" exists only for q a root of unity (q(N) = 1) and contains undetermined parameters. The 'string solution' exists for generic values of q (q(N) not equal 1). In this Letter we will explicitly construct the representation of the q-deformed algebra for generic values of q (q(N) not equal 1) and it is shown that the allowed range of the value of q + q must be restricted for each fixed N. (c) 2006 Elsevier B.V. All rights reserved. - R Nakayama, Y ShimonoPROGRESS OF THEORETICAL PHYSICS 112 (5) 883 - 894 0033-068X 2004/11 [Refereed][Not invited]

In a previous paper (hep-th/0402010) we proposed a matrix configuration for a non-commutative S-4 (NC4S) and constructed a non-commutative (star) product for field theories on NC4S. In the present paper we will show that any matrix can be expanded in terms of the matrix configuration representing NC4S just like any matrix can be expanded into symmetrized products of the matrix configuration for non-commutative S-2. Then a scalar field theory on NC4S is constructed. Our matrix configuration describes two S-4 joined at the circle and the Matrix theory action contains a projection matrix inside the trace to restrict the space of matrices to that for one S-4. - R Nakayama, Y ShimonoNUCLEAR PHYSICS B 693 (1-3) 176 - 194 0550-3213 2004/08 [Refereed][Not invited]

We present a matrix theory action and matrix configurations for spherical 4-branes. The dimension of the representations is given by N = 2(2j + 1) (j = 1/2, 1, 3/2,...). The algebra which defines these configurations is not invariant under SO(5) rotations but under SO(3) circle times SO(2). We also construct a non-commutative product star for field theories on S-4 in terms of that on S-2. An explicit formula of the non-commutative product which corresponds to the N = 4 dim representation of the non-commutative S-4 algebra is worked out. Because we use S-2 circle times S-2 parametrization of S-4, our S-4 is doubled and the non-commutative product and functions on S-4 are indeterminate on a great circle (S-1) on S-4. We will however, show that despite this mild singularity it is possible to write down a finite action integral of the non-commutative field theory on S-4. NS-NS B field background on S-4 which is associated with our matrix S-4 configurations is also constructed. (C) 2004 Elsevier B.V. All rights reserved. - K Hayasaka, R Nakayama, Y TakayaPHYSICS LETTERS B 553 (1-2) 109 - 118 0370-2693 2003/01 [Refereed][Not invited]

We obtain a new explicit expression for the noncommutative (star) product on the fuzzy two-sphere which yields a unitary representation. This is done by constructing a star product, *(lambda), for an arbitrary representation of SU(2) which depends on a continuous parameter X and searching for the values of; which give unitary representations. We will find two series of values: lambda = lambda(j)((A)) = 1/(2j) and lambda = lambda(j)((B)) = -1/(2j + 2), where j is the spin of the representation of SU(2). At lambda = lambda(j)((A)) the new star product *(lambda) has poles. To avoid the singularity the functions on the sphere must be spherical harmonics of order l less than or equal to 2j and then *(lambda) reduces to the star product * obtained by Presnajder [hep-th/9912050]. The star product at lambda = lambda(j)((B)), to be denoted by circle, is new. In this case the functions on the fuzzy sphere do not need to be spherical harmonics of order l less than or equal to 2j. The star product *(lambda) has no singularity for negative values of lambda and we can move from one representation lambda = lambda(j)((B)) to another lambda = lambda(j')((B)) smoothly on the negative lambda line. Because in this case there is no cutoff on the order of spherical harmonics, the degrees of freedom of the gauge fields on the fuzzy sphere coincide with those on the commutative sphere. Therefore, although the field theory on the fuzzy sphere is a system with finite degrees of freedom, we can expect the existence of the Seiberg-Witten map between the noncommutative and commutative descriptions of the gauge theory on the sphere. We will derive the first few terms of the Seiberg-Witten map for the U(1) gauge theory on the fuzzy sphere by using power expansion around the commutative point lambda = 0. (C) 2002 Elsevier Science B.V. All rights reserved. - K Hayasaka, R NakayamaNUCLEAR PHYSICS B 624 (1-2) 307 - 326 0550-3213 2002/03 [Refereed][Not invited]

We point out that when a D-brane is placed in an NS-NS B field background with nonvanishing field strength (H = dB) along the D-brane worldvolume, the coordinate of one end of the open string does not commute with that of the other in the low energy limit. The degrees of the freedom associated with both ends are not decoupled and accordingly, the effective action must be quite different from that of the ordinary noncommutative gauge theory for a constant B background. We construct an associative and noncommutative product star which operates on the coordinates of both ends of the string and propose a new type of noncommutative gauge action for the low energy effective theory of a Dp-brane. This effective theory is bi-local and lives in twice as large dimensions (2D = 2(p + 1)) as in the 11 = 0 case. When viewed as a theory in the D-dimensional space, this theory is nonlocal and we must force the two ends of the string to coincide. We will then propose a prescription for reducing this bi-local effective action to that in D dimensions and obtaining a local effective action. (C) 2002 Elsevier Science B.V. All rights reserved. - K Hayasaka, R NakayamaPHYSICS LETTERS B 463 (2-4) 181 - 187 0370-2693 1999/09 [Refereed][Not invited]

It is shown that the effective theory of D-particles has conformal symmetry with field-dependent parameters. This is a consequence of the supersymmetry. The string coupling constant is not transformed in contrast with the recent proposal of generalized conformal symmetry by Jevicki et al. [A. Jevicki, T. Yoneya, Nucl. Phys. B 535 (1998) 5072 (hep-th/9805069); A. Jevicki, Y. Kazama, T. Yoneya, hep-th/9810146]. This conformal symmetry can also be generalized to other Dp-brane systems. (C) 1999 Elsevier Science B.V. All rights reserved. **The Hamilton-Jacobi equations for strings and p-branes**Y Hosotani, R NakayamaMODERN PHYSICS LETTERS A 14 (28) 1983 - 1988 0217-7323 1999/09 [Refereed][Not invited]

Simple derivation of the Hamilton-Jacobi equation for bosonic strings and p-branes is given. The motions of classical strings and p-branes are described by two and p + 1 local fields, respectively. A variety of local field equations which reduce to the Hamilton-Jacobi equation in the classical limit are given. They are essentially nonlinear, having no linear term.- J Ambjorn, K Hayasaka, R NakayamaMODERN PHYSICS LETTERS A 12 (17) 1241 - 1266 0217-7323 1997/06 [Refereed][Not invited]

We studied the lowest order quantum corrections to the macroscopic wave functions Gamma(A,l) of non-critical string theory using the semiclassical expansion of Liouville theory. By carefully taking the perimeter constraint into account we obtained a new type of boundary condition for the Liouville field which is compatible with the reparametrization invariance of the boundary and which is not only a mixture of Dirichlet and Neumann types but also involves an integral of an exponential of the Liouville field along the boundary. This condition contains an unknown function of A/l(2). We determined this function by computing part of the one-loop corrections to Gamma(A,l). **New Loop Equations in Ising Model Coupled to 2d Gravity and String Field Theory**R. Nakayama, T. SuzukiProceeding of the Workshop "Frontiers in Quantum Field Theory" 126 - 135 1996 [Not refereed][Not invited]- R. Nakayama, T. SuzukiPhysical Review D54 (6) 3985 - 3394 1996 [Refereed][Not invited]
- R NAKAYAMA, T SUZUKIPHYSICS LETTERS B 354 (1-2) 69 - 77 0370-2693 1995/07 [Refereed][Not invited]

We investigate the integrability of the Schwinger-Dyson equations in c = 1 - 6/m(m+1) string field theory which were proposed by Ikehara et al. as the continuum limit of the Schwinger-Dyson equations of the matrix chain model. We show the continuum Schwinger-Dyson equations generate a closed algebra. This algebra contains Virasoro algebra but does nor coincide with W-infinity algebra. We include in the Schwinger-Dyson equations a new process of removing from the loop boundaries the operator H(sigma) which locally changes the spin configuration We also derive the string field Hamiltonian from the continuum Schwinger-Dyson equations. Its form is universal for all c = 1 - 6/m(m+1) string theories. **A NOTE ON STRING FIELD-THEORY IN THE TEMPORAL GAUGE**M IKEHARA, N ISHIBASHI, H KAWAI, T MOGAMI, R NAKAYAMA, N SASAKURAPROGRESS OF THEORETICAL PHYSICS SUPPLEMENT 118 (118) 241 - 257 0375-9687 1995 [Refereed][Not invited]

In this note, we review the recent developments in the string field theory in the temporal gauge.- M IKEHARA, N ISHIBASHI, H KAWAI, T MOGAMI, R NAKAYAMA, N SASAKURAPHYSICAL REVIEW D 50 (12) 7467 - 7478 0556-2821 1994/12 [Refereed][Not invited]
- R NAKAYAMAPHYSICS LETTERS B 325 (3-4) 347 - 353 0370-2693 1994/04 [Refereed][Not invited]

A two-loop (cylinder) amplitude of the 2d pure gravity theory is obtained in the proper-time gauge (g00 = 1, g01 = g10 = 0) in the continuum formulation. The constraint T01 = 0 is solved and used to reduce the problem of field theory to that of quantum mechanics. This reduction can also be proved by using a conformal Ward identity. The amplitude depends on the lengths l1, l2 of the boundaries, the proper time T and a non-negative integer m associated with winding modes around the boundaries. - H. Kawai, R. NakayamaPhysics Letters 306B (3, 4) 224 - 232 1993 [Refereed][Not invited]
- M. Fukuma, H, Kawai, R. NakayamaCommunications in Mathematical Physics 148 (1) 101 - 116 1992 [Refereed][Not invited]
- M. Fukuma, H. Kawai, R. NakayamaCommunications in Mathematical Physics 143 (2) 371 - 403 1992 [Refereed][Not invited]
- M. Fukuma, H. Kawai, R. NakayamaInternational Journal of Modern Physics A6 (8) 1385 - 1406 1991 [Refereed][Not invited]
- J GRUNDBERG, R NAKAYAMAMODERN PHYSICS LETTERS A 4 (1) 55 - 60 0217-7323 1989/01 [Refereed][Not invited]
- J GRUNDBERG, R NAKAYAMANUCLEAR PHYSICS B 306 (3) 497 - 515 0550-3213 1988/08 [Refereed][Not invited]
- P DIVECCHIA, R NAKAYAMA, JL PETERSEN, SIDENIUS, JR, S SCIUTONUCLEAR PHYSICS B 287 (4) 621 - 657 0550-3213 1987/06 [Refereed][Not invited]
**Covariant quantization of the bosonic string : Interacting theory**P. Di Vecchia, R. nakayamaProgress of the Paris-Meudon Colloguium 22-26sep1986. eds. H.J.de Vega and N. Sanchez, World Scientific 68 - 75 1987 [Refereed][Not invited]- P. Di Vecchia, R. Nakayama, J. L, Petersen, ans, S. SciutoNuclear Physics B282 (1) 103 - 124 1987 [Refereed][Not invited]
- P DIVECCHIA, R NAKAYAMA, JL PETERSEN, J SIDENIUS, S SCIUTOPHYSICS LETTERS B 182 (2) 164 - 168 0370-2693 1986/12 [Refereed][Not invited]
- Y KAZAMA, R NAKAYAMAPHYSICAL REVIEW D 32 (10) 2500 - 2510 0556-2821 1985 [Refereed][Not invited]
**Monte-Carlo simulation of 2 dimensional random surfaces**T. Eguchi, R. Nakayama, S.-K. YangNuclear Physics B251 [FS13] (3) 401 - 413 1985 [Refereed][Not invited]- R NAKAYAMA, Y OKADAPHYSICS LETTERS B 134 (3-4) 241 - 244 0370-2693 1984 [Refereed][Not invited]
- T EGUCHI, R NAKAYAMAPHYSICS LETTERS B 126 (1-2) 89 - 93 0370-2693 1983 [Refereed][Not invited]
- T EGUCHI, R NAKAYAMAPHYSICS LETTERS B 122 (1) 59 - 62 0370-2693 1983 [Refereed][Not invited]
- R NAKAYAMAPHYSICAL REVIEW D 28 (4) 922 - 935 0556-2821 1983 [Refereed][Not invited]
- H KAWAI, R NAKAYAMAPHYSICS LETTERS B 113 (4) 329 - 334 0370-2693 1982 [Refereed][Not invited]
**Comparison of the lattice Λ parameter with the continuum Λ parameter in massless QCD**H. Kawai, R. Nakayama, K. SeoNuclear Physics B189 (1) 40 - 62 1981 [Refereed][Not invited]

**量子重力理論および超弦理論の研究**科学研究費補助金**Study of quantum gravity theory and superstring theory**Grant-in-Aid for Scientific Research

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