arXiv subjects

H. Itoyama

Publications and source records attributed to H. Itoyama.

At least 73 records · Page 4Linked to original sources

arXiv1998

USp(2k) Matrix Model: Nonperturbative Approach to Orientifolds

We discuss theoretical implications of the large k USp(2k) matrix model in zero dimension. The model appears as the matrix model of type IIB superstrings on a large $T^{6}/Z^{2}$ orientifold via the matrix twist operation. In the small volume limit, the model behaves four dimensional and its T dual is six-dimensional worldvolume theory of type I superstrings in ten spacetime dimensions. Several theoretical considerations including the analysis on planar diagrams, the commutativity of the projectors with supersymmetries and the cancellation of gauge anomalies are given, providing us with the rationales for the choice of the Lie algebra and the field content. A few classical solutions are constructed which correspond to Dirichlet p-branes and some fluctuations are evaluated. The particular scaling limit with matrix T duality transformation is discussed which derives the F theory compactification on an elliptic fibered K3.

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arXiv1997

USp(2k) Matrix Model: F Theory Connection

We present a zero dimensional matrix model based on $USp(2k)$ with supermultiplets in symmetric, antisymmetric and fundamental representations. The four dimensional compactification of this model naturally captures the exact results of Sen \cite{Sen} in $F$ theory. Eight dynamical and eight kinematical supercharges are found, which is required for critical string interpretation. Classical vacuum has ten coordinates and is equipped with orbifold structure. We clarify the issue of spacetime dimensions which $F$ theory represented by this matrix model produces.

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arXiv1996

N=2 Supermultiplet of Currents and Anomalous Transformations in Supersymmetric Gauge Theory

We examine some properties of supermultiplet consisting of the U(1)_{J} current, extended supercurrents, energy-momentum tensor and the central charge in N=2 supersymmetric Yang-Mills theory. The superconformal improvement requires adding another supermultiplet beginning with the U(1)_{R} current. We determine the anomalous (quantum mechanical) supersymmetry transformation associated with the central charge and the energy-momentum tensor to one-loop order.

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arXiv1996

Infinity Cancellation, Type I' Compactification and String S-Matrix Functional

Nonvanishing tadpoles and possible infinities associated in the multiparticle amplitudes are discussed with regard to the disk and $RP^{2}$ diagrams of the Type I' compactification. We find that the infinity cancellation of $SO(32)$ type $I$ theory extends to this case as well despite the presence of tadpoles localized in the D-brane world-volume and the orientifold surfaces. Formalism of string S-matrix generating functional is presented to find a consistent string background as c-number source function: we find this only treats the cancellation of the tadpoles in the linearized approximation. Our formalism automatically provides representation of the string amplitudes on this background to all orders in $α'$.

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arXiv1996

Schwinger-Dyson and Large $N_{c}$ Loop Equation for Supersymmetric Yang-Mills Theory

We derive an infinite sequence of Schwinger-Dyson equations for $N=1$ supersymmetric Yang-Mills theory. The fundamental and the only variable employed is the Wilson-loop geometrically represented in $N=1$ superspace: it organizes an infinite number of supersymmetrizing insertions into the ordinary Wilson-loop as a single entity. In the large $N_{c}$ limit, our equation becomes a closed loop equation for the one-point function of the Wilson-loop average.

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arXiv1996

Integrability and Seiberg-Witten theory

A summary of results is presented, which provide exact description of the low-energy $4d$ $N=2$ and $N=4$ SUSY gauge theories in terms of $1d$ integrable systems.

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arXiv1995

Macroscopic $n$-Loop Amplitude for Minimal Models Coupled to Two-Dimensional Gravity: Fusion Rules and Interactions

We investigate the structure of the macroscopic $n$-loop amplitude obtained from the two-matrix model at the unitary minimal critical point $(m+1,m)$. We derive a general formula for the $n$-resolvent correlator at the continuum planar limit whose inverse Laplace transform provides the amplitude in terms of the boundary lengths $\ell_{i}$ and the renormalized cosmological constant $t$. The amplitude is found to contain a term consisting of $\left( \frac{\partial} {\partial t} \right)^{n-3}$ multiplied by the product of modified Bessel functions summed over their degrees which conform to the fusion rules and the crossing symmetry. This is found to be supplemented by an increasing number of other terms with $n$ which represent residual interactions of loops. We reveal the nature of these interactions by explicitly determining them as the convolution of modified Bessel functions and their derivatives for the case $n=4$ and the case $n=5$. We derive a set of recursion relations which relate the terms in the $n$-resolvents to those in the $(n-1)$-resolvents.

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arXiv1995

Prepotential and the Seiberg-Witten Theory

Some basic facts about the prepotential in the SW/Whitham theory are presented. Consideration begins from the abstract theory of quasiclassical $τ$-functions , which uses as input a family of complex spectral curves with a meromorphic differential $dS$, subject to the constraint $\partial dS/\partial(moduli)= \ holomorphic$, and gives as an output a homogeneous prepotential on extended moduli space. Then reversed construction is discussed, which is straightforwardly generalizable from spectral {\it curves} to certain complex manifolds of dimension $d >1$ (like $K3$ and $CY$ families). Finally, examples of particular $N=2$ SUSY gauge models are considered from the point of view of this formalism. At the end we discuss similarity between the $WP^{12}_{1,1,2,2,6}$ -\-Calabi-\-Yau model with $h_{21}=2$ and the $1d$ $SL(2)$ Calogero/Ruijsenaars model, but stop short of the claim that they belong to the same Whitham universality class beyond the conifold limit.

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arXiv1995

Integrability and Seiberg-Witten Theory: Curves and Periods

Interpretation of exact results on the low-energy limit of $4d$ $N=2$ SUSY YM in the language of $1d$ integrability theory is reviewed. The case of elliptic Calogero system, associated with the flow between $N=4$ and $N=2$ SUSY in $4d$, is considered in some detail.

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arXiv1995

Motions of the String Solutions in the XXZ Spin Chain under a Varying Twist

We determine the motions of the roots of the Bethe ansatz equation for the ground state in the XXZ spin chain under a varying twist angle. This is done by analytic as well as numerical study at a finite size system. In the attractive critical regime $ 0< Δ<1 $, we reveal intriguing motions of strings due to the finite size corrections to the length of the strings: in the case of two-strings, the roots collide into the branch points perpendicularly to the imaginary axis, while in the case of three-strings, they fluctuate around the center of the string. These are successfully generalized to the case of $n$-string. These results are used to determine the final configuration of the momenta as well as that of the phase shift functions. We obtain these as well as the period and the Berry phase also in the regime $ Δ\leq -1$, establishing the continuity of the previous results at $ -1 < Δ< 0 $ to this regime. We argue that the Berry phase can be used as a measure of the statistics of the quasiparticle ( or the bound state) involved in the process.

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arXiv1995

Macroscopoic Three-Loop Amplitudes and the Fusion Rules from the Two-Matrix Model

From the computation of three-point singlet correlators in the two-matrix model, we obtain an explicit expression for the macroscopic three-loop amplitudes having boundary lengths $\ell_{i}$ $(i = 1\sim 3)$ in the case of the unitary series $(p,q)= (m+1,m)$ coupled to two-dimensional gravity. The sum appearing in this expression is found to conform to the structure of the CFT fusion rules while the summand factorizes through a product of three modified Bessel functions. We briefly discuss a possible generalization of these features to macroscopic $n$-loop amplitudes.

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arXiv1994

Continuum Annulus Amplitude from the Two-Matrix Model

An explicit expression for continuum annulus amplitudes having boundary lengths $\ell_{1}$ and $\ell_{2}$ is obtained from the two-matrix model for the case of the unitary series; $(p,q) = (m + 1, m)$. In the limit of vanishing cosmological constant, we find an integral representation of these amplitudes which is reproduced, for the cases of the $m = 2~(c=0)$ and the $m \rightarrow \infty~(c=1)$, by a continuum approach consisting of quantum mechanics of loops and a matter system integrated over the modular parameter of the annulus. We comment on a possible relation to the unconventional branch of the Liouville gravity.

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arXiv1994

Multicritical Behavior of $c=1$ Matrix Model

We discuss multicritical behavior of $c=1$ matrix model, extending the recent work of ref. \cite{CIO} on a nonperturbative completion of the density of states function. For the odd orders of multicriticality, we are able to determine the higher genus contributions and a nonperturbative completion from the WKB wave function of the multicritical periodic potential. The expression for the contributions as a function of the scaled chemical potential is found to be the same as the one at the lowest critical point. We point out a strange scaling behavior.

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arXiv1993

Sine-Gordon Theory with Higher Spin $N=2$ Supersymmetry and the Massless Limit

The Sine-Gordon theory at $\frac{β^{2}}{8π} = \frac{2}{(2n+3)},\; n= 1,2,3 \cdots $ has a higher spin generalization of the $N=2$ supersymmetry with the central terms which arises from the affine quantum group $U_{q}( \hat{s \ell} (2))$. Observing that the algebraic determination of $S$ matrices $( \approx {\rm quantum~ integrability })$ requires the saturation of the generalized Bogomolny bound, we construct a variant of the Sine-Gordon theory at this value of the coupling in the framework of $S$ matrix theory. The spectrum consists of a doublet of fractionally charged solitons as well as that of anti-solitons in addition to the ordinary breathers. The construction demonstrates the existence of the theory other than the one by the truncation to the breathers considered by Smirnov. The allowed values for the fractional part of the fermion number is also determined. The central charge in the massless limit is found to be $c= 1$ from the TBA calculation for nondiagonal S matrices. The attendant $c=1$ conformal field theory is the gaussian model with ${\bf Z_{2}}$ graded chiral algebra at the radius parameter $r= \sqrt{2n+3}$. In the course of the calculation, we find $4n+2$ zero modes from the (anti-)soliton distributions.

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arXiv1993

Universal and Nonperturbative Behavior in the One-Plaquette Model of Two-Dimensional String Theory

The one-plaquette Hamiltonian of large N lattice gauge theory offers a constructive model of a $1+1$-dimensional string theory with a stable ground state. The free energy is found to be equivalent to the partition function of a string where the world sheet is discretized by even polygons with signature and the link factor is given by a non-Gaussian propagator. At large, but finite, N we derive the nonperturbative density of states from the WKB wave function and the dispersion relations. This is expressible as an infinite, but convergent, series with the inverse of the hypergeometric function replacing the harmonic oscillator spectrum of the $1+1$-dimensional string. In the scaling limit, the series is shown to be finite, containing both the perturbative (asymptotic) expansion of the inverted harmonic oscillator model, and a nonperturbative piece that survives the scaling limit.

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arXiv1992

Integrable Superhierarchy of Discretized 2d Supergravity

The hierarchical nonlinear super-differential equations are identified which describe universal behavior of the discretized model of $2d$ supergravity recently proposed. This is done by first taking a double scaling limit of the super Virasoro constraints ( at finite $N$) of the model and by rederiving it from the $\tilde{G}_{-1/2}$ constraint and the two reduction of the super KP hierarchy discussed. The double-scaled constraints are found to be described by a twisted scalar and a Ramond fermion.

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arXiv1992

Anomalous Transformation in Supersymmetric Yang-Mills Theory

An ``anomalous'' supersymmetry transformation of the gaugino axial current is given in supersymmetric Yang-Mills theory. The contact term is computed to one-loop order by a gauge-invariant point-splitting procedure. We reexamine the supercurrent anomaly in this method.

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arXiv1991

Superloop Equations and Two Dimensional Supergravity

We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of $(2,4m)$-minimal superconformal models coupled to $2D$-supergravity. The basic assumption in our presentation is a set of super-Virasoro constraints imposed on the partition function. We recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also able to evaluate all planar loop correlation functions in the continuum limit. We find evidence to identify the integrable hierarchy of non-linear equations describing the double scaling limit as a supersymmetric generalization of KP studied by Rabin.

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