A conjectural generating function for numbers of curves on surfaces

I give a conjectural generating function for the numbers of $\delta$-nodal curves in a linear system of dimension $\delta$ on an algebraic surface. It reproduces the results of Vainsencher for the case $\delta\le 6$ and Kleiman-Piene for the case $\delta\le 8$. The numbers of curves are expressed in terms of five universal power series, three of which I give explicitly as quasimodular forms. This gives in particular the numbers of curves of arbitrary genus on a K3 surface and an abelian surface in terms of quasimodular forms, generalizing the formula of Yau-Zaslow for rational curves on K3 surfaces. The coefficients of the other two power series can be determined by comparing with the recursive formulas of Caporaso-Harris for the Severi degrees in $\P_2$. We verify the conjecture for genus 2 curves on an abelian surface. We also discuss a link of this problem with Hilbert schemes of points.Comment: amslatex 13 page

On the Twisted N=2N=2 Superconformal Structure in 2d2d Gravity Coupled to Matter

It is shown that the two dimensional gravity, described either in the conformal gauge (the Liouville theory) or in the light cone gauge, when coupled to matter possesses an infinite number of twisted $N=2$ superconformal symmetries. The central charges of the $N=2$ algebra for the two gauge choices are in general different. Further, it is argued that the physical states in the light cone gauge theory can be obtained from the Liouville theory by a field redefinition.Comment: Plain Tex, 13 pages, IC/93/81, UG-3/9

Neutrinos with Zee-Mass Matrix in Vacuum and Matter

Neutrino mass matrix generated by the Zee (radiative) mechanism has zero (in general, small) diagonal elements and a natural hierarchy of the nondiagonal elements. It can be considered as an alternative (with strong predictive power) to the matrices generated by the see-saw mechanism. The propagation in medium of the neutrinos with the Zee-mass matrix is studied. The flavor neutrino transitions are described analytically. In the physically interesting cases the probabilities of transitions as functions of neutrino energy can be represented as two-neutrino probabilities modulated by the effect of vacuum oscillations related to the small mass splitting. Possible applications of the results to the solar, supernova, atmospheric and relic neutrinos are discussed. A set of the predictions is found which could allow to identify the Zee-mass matrix and therefore the corresponding mechanism of mass generation.Comment: 25 pages (3 figures available upon request), LaTeX, IC/94/4

Out of Equilibrium Phase Transitions and a Toy Model for Disoriented Chiral Condensates

We study the dynamics of a second order phase transition in a situation thatmimics a sudden quench to a temperature below the critical temperature in a model with dynamical symmetry breaking. In particular we show that the domains of correlated values of the condensate grow as $\sqrt{t}$ and that this result seems to be largely model independent.Comment: 17 pages, UR-1315 ER-40685-76

Absence of Higher Order Corrections to Noncommutative Chern-Simons Coupling

We analyze the structure of noncommutative pure Chern-Simons theory systematically in the axial gauge. We show that there is no IR/UV mixing in this theory in this gauge. In fact, we show, using the usual BRST identities as well as the identities following from vector supersymmetry, that this is a free theory. As a result, the tree level Chern-Simons coefficient is not renormalized. It also holds that the Chern-Simons coefficient is not modified at finite temperature. As a byproduct of our analysis, we prove that the ghosts completely decouple in the axial gauge in a noncommutative gauge theory.Comment: LaTeX file, 16 pages, no figur

Boundary Dynamics in Dilaton Gravity

We study the dynamics of the boundary dilaton gravity coupled to N massles scalars. We rederive the boundary conditions of [1] and [3] in a way which makes the requirement of reparametrization invariance and role of conformal anomaly explicit. We then study the semiclassical behaviour of the boundary in the N = 24 theory in the presence of an incoming matter wave with a constant energy flux spreaded over a finite interval. There is a critical value of the matter energy density below which the boundary is stable and all the matter is reflected back. For energy densities greater than this critical value there is a similar behaviour for small values of total energy thrown in. However, when the total energy exceeds another critical value, the boundary exibits a runaway behaviour and the spacetime devolopes singularities and horizons.Comment: 16 pages, Latex file, TIFR/TH/94-24, IC/94/147 (preprint numbers are included

Abrikosov Vortex and Branes

We give a brief review of the application of some topological solutions in field theory.Comment: To appear in a volume in honour of A.P.Balchandran in occasion of his 65th birthday. Spelling of the name in the title and some other typos correcte

Density-dependent phonoriton states in highly excited semiconductors

The dynamical aspects of the phonoriton state in highly-photoexcited semiconductors is studied theoretically. The effect of the exciton-exciton interaction and nonbosonic character of high-density excitons are taken into account. Using Green's function method and within the Random Phase Approximation it is shown that the phonoriton dispersion and damping are very sensitive to the exciton density, characterizing the excitation degree of semiconductors.Comment: ICTP preprint IC/95/226, Latex, 10 pages, 3 figure

Mesoscopic Kondo screening effect in a single-electron transistor embedded in a metallic ring

We study the Kondo screening effect generated by a single-electron transistor or quantum dot embedded in a small metallic ring. When the ring circumference $L$ becomes comparable to the fundamental length scale $\xi_K^0=\hbar \upsilon _F/T_K^0$ associated with the {\it bulk} Kondo tempe the Kondo resonance is strongly affected, depending on the total number of electrons ({\it modulo} 4) and magnetic flux threading the ring. The resulting Kondo-assisted persistent currents are also calculated in both Kondo and mixed valence regimes, and the maximum values are found in the crossover region.Comment: 4 pages, Revtex, 6 figures, more references are include

Optical Conductivity in the Copper Oxide Materials

The frequency- and temperature-dependent optical conductivity of the copper oxide materials in the underdoped and optimal doped regimes are studied within the t-J model. The conductivity spectrum shows the unusual behavior at low energies and anomalous midinfrared peak in the low temperatures. However, this midinfrared peak is severely depressed with increasing temperatures, and vanishes at higher temperatures.Comment: 11 pages, Revtex, Two figures are not included, and can be obtained by reques