arXiv subjects

Hisao Suzuki

Publications and source records attributed to Hisao Suzuki.

33 records · Page 2Linked to original sources

arXiv1998

Theory of Current-Induced Breakdown of the Quantum Hall Effect

By studying the quantum Hall effect of stationary states with high values of injected current using a von Neumann lattice representation, we found that broadening of extended state bands due to a Hall electric field occurs and causes the breakdown of the quantum Hall effect. The Hall conductance agrees with a topological invariant that is quantized exactly below a critical field and is not quantized above a critical field. The critical field is proportional to $B^{3/2}$ and is enhanced substantially if the extended states occupy a small fraction of the system.

cond-mat.mes-hall↗

arXiv1998

Perturbations of Kerr-de Sitter Black Hole and Heun's Equations

It is well known that the perturbation equations of massless fields for the Kerr-de Sitter geometry can be written in the form of separable equations. The equations have five definite singularities so that the analysis has been expected to be difficult. We show that these equations can be transformed to Heun's equations, for which we are able to use known technique for the analysis of the solutions. We reproduce results known previously for the Kerr geometry and de Sitter geometry in the confluent limits of the Heun's functions. Our analysis applies can be extended to Kerr-Newman-de Sitter geometry for massless fields with spin 0 and 1/2.

gr-qc↗

arXiv1997

Evaluation of Periods via Fibrations in Seiberg-Witten Theories and in Type-II String

We show how to evaluate the periods in Seiberg-Witten theories and in K3-fibered Calabi-Yau manifolds by using fibrations of the theories. In the Seiberg-Witten theories, it is shown that the dual pair of fields can be constructed from the classical fields in a simple form. As for Calabi-Yau manifolds which are fibrations of K3 surface, we obtain the solutions of the Picard-Fuchs equations from the periods of K3 surface. By utilizing the expression of periods for two-parameter models of type-II string, we derive the solutions of the Picard-Fuchs equations around the points of enhanced gauge symmetry and show a simple connection to the SU(2) Seiberg-Witten theory.

hep-th↗

arXiv1997

Seiberg-Witten Theory of Rank Two Gauge Groups and Hypergeometric Series

In SU(2) Seiberg-Witten theory, it is known that the dual pair of fields are expressed by hypergeometric functions. As for the theory with SU(3) gauge symmetry without matters, it was shown that the dual pairs of fields can be expressed by means of the Appell function of type F_4. These expressions are convenient for analyzing analytic properties of fields. We investigate the relation between Seiberg-Witten theory of rank two gauge group without matters and hypergeometric series of two variables. It is shown that the relation between gauge theories and Appell functions can be observed for other classical gauge groups of rank two. For B_2 and C_2, the fields are written in terms of Appell functions of type H_5. For D_2, we can express fields by Appell functions of type F_4 which can be decomposed to two hypergeometric functions, corresponding to the fact SO(4)\sim SU(2)\times SU(2). We also consider the integrable curve of type C_2 and show how the fields are expressed by Appell functions. However in the case of exceptional group G_2, our examination shows that they can be represented by hypergeometric series which does not correspond to the Appell functions.

hep-th↗

arXiv1997

Enhanced Gauge Symmetry in Three-Moduli Models of Type-II String and Hypergeometric Series

The conifold singularities in the type-II string are considered as the points of phase transition. In some cases, these singularities can be understood in the framework of the conventional fields theores as the points of enhanced gauge symmetry. We consider a class of three moduli Type-II strings. It is shown the periods can be written in the form of hypergeometric series around the singular points in these models. The leading expansion around the conifold locus turns out to be described by Appell functions. In one singular point, we observe the enhanced gauge symmetry of $SU(2)\times SU(2)$ independent of the models. Around another conifold locus, however, the resulting expression of the Appell functions depends on the models. We examine the result by considering a relation between these Appell functions and underlying Riemann surfaces.

hep-th↗

arXiv1996

On Explicit Evaluations Around the Conformal Point in N=2 Supersymmetric Yang-Mills Theories

We show how to give the expression for periods, Higgs field and its dual of N=2 supersymmetric Yang-Mills theory around the conformal point. This is achieved by evaluating the integral representation in the weak coupling region, and by using analytic continuation to the conformal point. The explicit representation is shown for the SU(2) theory with matter fields and also for pure SU(N) and pure SO(2N) theory around the conformal point where the relation to the beta function of the theory is clarified. We also discuss a relation between the fixed points in the SU(2) theories with matter fields and the Landau-Ginzburg point of 2-D N=2 SCFT.

hep-th↗

arXiv1996

Periods and Prepotential of N=2 SU(2) Supersymmetric Yang-Mills Theory with Massive Hypermultiplets

We derive a simple formula for the periods associated with the low energy effective action of $N=2$ supersymmetric $SU(2)$ Yang-Mills theory with massive $N_f\le 3$ hypermultiplets. This is given by evaluating explicitly the integral associated to the elliptic curve using various identities of hypergeometric functions. Following this formalism, we can calculate the prepotential with massive hypermultiplets both in the weak coupling region and in the strong coupling region. In particular, we show how the Higgs field and its dual field are expressed as generalized hypergeometric functions when the theory has a conformal point.

hep-th↗

arXiv1996

Prepotential of $N=2$ Supersymmetric Yang-Mills Theories in the Weak Coupling Region

We show how to obtain the explicite form of the low energy quantum effective action for $N=2$ supersymmetric Yang-Mills theory in the weak coupling region from the underlying hyperelliptic Riemann surface. This is achieved by evaluating the integral representation of the fields explicitly. We calculate the leading instanton corrections for the group $SU(\nc), SO(N)$ and $SP(2N)$ and find that the one-instanton contribution of the prepotentials for the these group coincide with the one obtained recently by using the direct instanton caluculation.

hep-th↗

arXiv1996

Analytic Solutions of the Regge-Wheeler Equation and the Post-Minkowskian Expansion

Analytic solutions of the Regge-Wheeler equation are presented in the form of series of hypergeometric functions and Coulomb wave functions which have different regions of convergence. Relations between these solutions are established. The series solutions are given as the Post-Minkowskian expansion with respect to a parameter $ε\equiv 2Mω$, $M$ being the mass of black hole. This expansion corresponds to the post-Newtonian expansion when they are applied to the gravitational radiation from a particle in circular orbit around a black hole. These solutions can also be useful for numerical computations.

gr-qc↗

arXiv1996

Integral Equations of Fields on the Rotating Black Hole

It is known that the radial equation of the massless fields with spin around Kerr black holes cannot be solved by special functions. Recently, the analytic solution was obtained by use of the expansion in terms of the special functions and various astrophysical application have been discussed. It was pointed out that the coefficients of the expansion by the confluent hypergeometric functions are identical to those of the expansion by the hypergeometric functions. We explain the reason of this fact by using the integral equations of the radial equation. It is shown that the kernel of the equation can be written by the product of confluent hypergeometric functions. The integral equaton transforms the expansion in terms of the confluent hypergeometric functions to that of the hypergeometric functions and vice versa,which explains the reason why the expansion coefficients are universal.

gr-qc↗

arXiv1996

Analytic Solutions of the Teukolsky Equation and their Low Frequency Expansions

Analytic solutions of the Teukolsky equation in Kerr geometries are presented in the form of series of hypergeometric functions and Coulomb wave functions. Relations between these solutions are established. The solutions provide a very powerful method not only for examining the general properties of solutions and physical quantities when they are applied to, but also for numerical computations. The solutions are given in the expansion of a small parameter $ε\equiv 2Mω$, $M$ being the mass of black hole, which corresponds to Post-Minkowski expansion by $G$ and to post-Newtonian expansion when they are applied to the gravitational radiation from a particle in circular orbit around a black hole. It is expected that these solutions will become a powerful weapon to construct the theoretical template towards LIGO and VIRGO projects.

gr-qc↗

arXiv1995

Calabi-Yau Compactification of Type-IIB string and a Mass Formula of the Extreme Black Holes

Recently proposed mechanism of the black hole condensation at conifold singularity in type II string is an interesting idea from which we can interpret the phase of the universal moduli space of the string vacua. It might also be expected that the true physics is on the conifold singularity after supersymmetry breaking. We derive a mass formula for the extreme black holes caused by the self-dual 5-form field strength, which is stable and supersymmetric. It is shown that the formula can be written by the moduli parameters of Calabi-Yau manifold and can be calculated explicitly.

hep-th↗

arXiv1994

On Bogoliubov Transformation of Scalar Wave Functions in De Sitter Space

We discuss the Bogoliubov transformation of the scalar wave functions caused by the change of coordinates in 4 dimensional de Sitter space. It is shown that the exact Bogoliubov coefficients can be obtained from the global coordinates to the static coordinates where there exist manifest horizon. We consider two type of global coordinates. In one global coordinates, it is shown that the Bogoliubov transformation to the static coordinates can be expressed by the discontinuous integral of Weber and Schafheitlin. The positive and negative energy states in the global coordinates degenerate in the static coordinates. In the other global coordinates, we obtain the Bogoliubov coefficients by using the analytic continuation of the hypergeometric functions in two variables.

hep-th↗

arXiv1993

Bosonization of a Topological Coset Model and Non-Critical String Theory

We analyze the relation between a topological coset model based on super $SL(2,R)/U(1)$ coset and non-critical string theory by using free field realization. We show that the twisted $N=2$ algebra of the coset model can be naturally transformed into that of non-critical string. The screening operators of the coset models can be identified either with those of the minimal matters or with the cosmological constant operator. We also find that another screening operator, which is intrinsic in our approach, becomes the BRST nontrivial state of ghost number $0$ (generator of the ground ring for $c=1$ gravity).

hep-th↗

arXiv1992

Interactions of Discrete States with Nonzero Ghost Number \\ in $c=1$ $2D$ Gravity

We study the interactions of the discrete states with nonzero ghost number in $c=1$ two-dimensional ($2D$) quantum gravity. By using the vertex operator representations, it is shown that their interactions are given by the structure constants of the group of the area preserving diffeomorphism similar to those of vanishing ghost number. The effective action for these states is also worked out. The result suggests the whole system has a BRST-like symmetry.

hep-th↗