6,128 research outputs found

### 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 $N=2$ Superconformal Structure in $2d$ 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

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