arXiv subjects

Ryuichi Nakayama

Publications and source records attributed to Ryuichi Nakayama.

26 records · Page 2Linked to original sources

arXiv2004

Non-commutative Field Theory on S^4

In the 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's 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.

hep-th↗

arXiv2002

An Associative and Noncommutative Product for the Low Energy Effective Theory of a D-Brane in Curved Backgrounds and Bi-Local Fields

We point out that when a D-brane is placed in an NS-NS B field background with non-vanishing 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 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 H=0 case. When viewed as a theory in the D-dimensional space, this theory is non-local 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.

hep-th↗

arXiv1999

Conformal Invariance of the D-Particle Effective Action

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 symmtery by Jevicki et al. This conformal symmetry can also be generalized to other Dp-brane systems.

hep-th↗

arXiv1999

The Hamilton-Jacobi Equations for Strings and p-Branes

Simple derivation of the Hamilton-Jacobi equation for bosonic strings and p-branes is given. The motion of classical strings and p-branes is 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.

hep-th↗

arXiv1996

Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory

New loop equations for all genera in $c = \frac{1}{2}$ non-critical string theory are constructed. Our loop equations include two types of loops, loops with all Ising spins up (+ loops) and those with all spins down ( $-$ loops). The loop equations generate an algebra which is a certain extension of $W_3$ algebra and are equivalent to the $W_3$ constraints derived before in the matrix-model formulation of 2d gravity. Application of these loop equations to construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is considered.

hep-th↗

arXiv1995

Integrability of Schwinger-Dyson Equations in 2D Quantum Gravity and c < 1 Non-critical String Field Theory

We investigate the integrability of the Schwinger-Dyson equations in $c = 1 - \frac{6}{m(m+1)}$ 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 not coincide with $W_{\infty}$ algebra. We include in the Schwinger-Dyson equations a new process of removing from the loop boundaries the operator ${\cal H}(σ)$ 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 $c = 1 - \frac{6}{m(m+1)}$ string theories.

hep-th↗

arXiv1993

2D Quantum Gravity in the Proper-Time Gauge

A two-loop (cylinder) amplitude of the 2d pure gravity theory is obtained in the proper-time gauge ($g_{00}=1$, $g_{01}=g_{10}=0$) in the continuum formulation. The constraint $T_{01}=0$ 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 $l_1, l_2$ of the boundaries, the proper time $T$ and a non-negative integer $m$ associated with winding modes around the boundaries.

hep-th↗

arXiv1993

Quantum $R^2$ Gravity in Two Dimensions

Two-dimensional quantum gravity with an $R^2$ term is investigated in the continuum framework. It is shown that the partition function for small area $A$ is highly suppressed by an exponential factor $exp \{ -2π(1-h)^2/(m^2A) \}$, where $1/m^2$ is the coefficient (times $32π$) of $R^2$ and $h$ is the genus of the surface. Although positivity is violated, at a short distance scale ( $\ll 1/m$) surfaces are smooth and the problem of the branched polymer is avoided.

hep-th↗