International Journal of Modern Physics A

In 1983, Donaldson shocked the topology world by using instantons from physics to prove new theorems about four-dimensional manifolds, and he developed new topological invariants. In 1988, Witten showed how these invariants could be obtained by correlation functions for a twisted N = 2 SUSY gauge theory. In 1994, Seiberg and Witten discovered dualities for such theories, and in particular, developed a new way of looking at four-dimensional manifolds that turns out to be easier, and is conjectured to be equivalent to, Donaldson theory.

This review describes the development of this mathematical subject, and shows how the physics played a pivotal role in the current understanding of this area of topology.

We write down one-to-one mappings between the singular vectors of the Neveu–Schwarz N = 2 superconformal algebra and 16 + 16 types of singular vectors of the topological and of the Ramond N = 2 superconformal algebras. As a result one obtains the construction formulae for the latter using Dörrzapf's construction formulae for the Neveu–Schwarz singular vectors. The indecomposable singular vectors of the topological and of the Ramond N = 2 algebras ("no-label" and "no-helicity" singular vectors) cannot be mapped to singular vectors of the Neveu–Schwarz N = 2 algebra, but to subsingular vectors, for which no construction formulae exist.

The dynamical fluctuations inside the quark and antiquark jets are studied using Monte Carlo method. Quark and antiquark jets are identified from the two-jet events in e⁺e^- collisions at 91.2 GeV by checking them at parton level. It is found that the transition point exists inside both of these two kinds of jets. At this point the jets are circular in the transverse plane with respect to the property of dynamical fluctuations. The results are consistent with the fact that the third jet (gluon jet) was historically first discovered in e⁺e^- collisions in the energy region 17–30 GeV.

We obtain exact solutions of Dirac equation for radial power-law relativistic potentials at rest mass energies. It turns out that these are the relativistic extension of a subclass of exact solutions of Schrödinger equation at zero energy carrying representations of SO(2,1) Lie algebra. The latter are obtained by point canonical transformations of the exactly solvable problem of the three dimensional oscillator. The wave function solutions are written in terms of the confluent hypergeometric functions and almost always square integrable. For most cases these solutions support bound states at zero energy. Some exceptional unbounded states are normalizable for nonzero angular momentum. Using a generalized definition, degeneracy of the nonrelativistic states is demonstrated and the associated degenerate observable is defined.

Presently there is preliminary observational evidence that the cosmological constant might be nonzero, and hence that our universe is eternally accelerating (de Sitter). This poses fundamental problems for string theory, since a scattering matrix is not well defined in such universes. In a previous paper we have presented a model, based on (nonequilibrium) noncritical strings, which is characterized by eventual "graceful" exit from a de Sitter phase. The model is based on a type-0 string theory, involving D3 brane worlds, whose initial quantum fluctuations induce the noncriticality. We argue in this paper that this model is compatible with the current observations. A crucial role for the correct "phenomenology" of the model is played by the relative magnitude of the flux of the five-form of the type 0 string to the size of five of the extra dimensions, transverse to the direction of the flux-field. We do not claim, at this stage at least, that this model is a realistic physical model for the universe, but we find it interesting that the model cannot be ruled out immediately, at least on phenomenological grounds.

Global geometric properties of dS space are presented explicitly in various coordinates. A Robertson–Walker-like metric is deduced, which is convenient to be used in the study of dynamics in dS space. Singularities of wave functions of massive scalar fields at boundary are demonstrated. A bulk-boundary propagator is constructed by making use of the solutions of equations of motion. The dS/CFT correspondence and the Strominger mass bound is shown.

We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.

The present paper aims at testing a very simple approach to interpret the characteristics of inclusive production of pions in high energy NA and AA collisions by a somewhat in-depth analysis of the same for NN interactions; and also at reporting here thus some interesting observations made on the nature of rapidity and transverse momentum spectra of the produced pions. And this approach is built upon a newly offered master formula holding the key for converting the results of high energy nucleon–nucleon (NN) collision to the corresponding observables on differential and inclusive cross-sections for both nucleon–nucleus and nucleus–nucleus (heavy ion) collisions in a generalized form. The proposed formulae, used in a somewhat phenomenological way, can provide modestly reliable parametrization of data in the broad range of collision energy and the varied range of projectile-target combinations. This opens up the possibility of understanding in a quite unified manner the large amount of data on the rapidity and transverse momentum spectra in a wide range of interactions and energies starting right from ISR, rather Bevelac, to the relativistic heavy ion collisions (RHIC) via the various collider scales of energy. The agreements between the data and calculations, in most cases, are quite satisfactory both qualitatively and quantitatively. While highlighting this success, the limitation of the approach has also been pointed out in the end as clearly and categorically as possible.