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.Comment: 10 gages, late

Interactions of Discrete States with Nonzero Ghost Number \\ in c=1c=1 2D2D 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.Comment: 10 pages, OS-GE 25-9

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.Comment: 20 pages, Late

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.Comment: 21 pages, LaTe

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.Comment: 16 pages, Latex, no figures, a reference correcte

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.Comment: 16 pages, OU-HET 202, LMU-TPW 94-1

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 $\epsilon \equiv 2M\omega$, $M$ 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.Comment: 22 page