International Journal of Modern Physics A

In the first part of the paper, I give a low-resolution overview of the current state of particle physics — the triumph of the Standard Model and its discontents. I review and re-endorse the remarkably direct and (to me) compelling argument that existing data, properly interpreted, point toward a unified theory of fundamental particle interactions and toward low-energy supersymmetry as the near-term future of high energy physics as a natural science. I then attempt, as requested, some more "visionary" — i.e. even lower resolution — comments about the farther future. In that spirit, I emphasize the continuing importance of condensed matter physics as a source of inspiration and potential application, in particular for expansion of symmetry concepts, and of cosmology as a source of problems, applications, and perhaps ultimately limitations.

In this work I present a numerical study of the Finite Size Scaling (FSS) of a correlation length in the framework of the CP^N-1 model by means of the 1/N expansion. This study has been thought as preparatory to the application of FSS to the measure on the lattice of a new coupling constant f_x(1/R), defined in terms or rectangular Wilson loops. I give also a perturbative expansion of f_x(1/R) in powers of the corresponding coupling constant in the scheme together with some preliminary numerical results obtained from the Polyakov ratio and I point out the conceptual problems that limit this approach.

Fractional strings in the spectrum of states of open strings attached to a multiply wound D-brane is explained. We first describe the fractional string states in the low energy effective theory where the topology of multiple winding is encoded in the gauge holonomy. The holonomy induces twisted boundary conditions responsible for the fractional moding of these states. We also describe fractional strings in world sheet formulation and compute simple scattering amplitudes for Hawking emission/absorption. Generalization to fractional DN-strings in a one-brane five-brane bound state is described. When a one-brane and a five-brane wraps Q₁ and Q₅ times respectively around a circle, the momentum of DN-strings is quantized in units of 2π/LQ₁Q₅. These fractional states appear naturally in the perturbative spectrum of the theory.

We examine the cooling mechanism of a nascent neutron star core by the emission of wrong helicity neutrinos, when the core is at the verge of pion condensation. We study the dominant process due to neutrino magnetic moment in terms of the model-independent multipole amplitudes based on dispersion relation theory. This calculation gives a more realistic emission rate for neutrinos and hence an upper bound for neutrino magnetic moment

A framework of second-quantization of D5-branes is proposed. It is based on the study of topology of the moduli space of their low energy effective world volume theory. Among the topological cycles whose resolve singularities caused by overlapping D5-branes, there are introduced those cycles which duals, constituting a subspace of cohomology group of the moduli space, turn out to define the Fock space of the second-quantized D5-branes. The second-quantized operators are given by creation and annihilation operators of those cycles or their duals.

Basic assumptions necessary for the proof of the CPT theorem are considered. It is found that the CPT theorem is not valid for a physical system with unstable particles decaying exponentially. The Lee, Oehme and Yang (LOY) model of neutral kaons decay is discussed and the conclusion is drawn that CPT-transformation cannot be a symmetry in a system which contains the LOY model as a subsystem, and, thus this model is shown to be incapable of describing possible CPT-violation effects correctly. The approximate formulae for matrix elements of the effective Hamiltonian H_‖ governing the time evolution in neutral kaons subspace (different from those obtained by means of the Weisskopf–Wigner method and used by LOY) and their implications for an interpretation of the standard CPT-violation parameter are considered. Within this approximation it is shown that in the system preserving CPT-symmetry and that δ=0 is possible only if , where H is the total Hamiltonian of the system under consideration, that is, if the system does not preserve CPT-symmetry.

We reinterpret the Faddeev–Popov gauge-fixing procedure of Yang–Mills theories as the definition of a topological quantum field theory for gauge group elements depending on a background connection. This has the advantage of relating topological gauge-fixing ambiguities to the global breaking of a supersymmetry. The global zero modes of the Faddeev–Popov ghosts are handled in the context of an equivariant cohomology without breaking translational invariance. The gauge-fixing involves constant fields which play the role of moduli and modify the behavior of Green functions at subasymptotic scales. At the one loop level physical implications from these power corrections are gauge invariant.

We exploit the identification between the critical theory of the three-state Potts model and the D₅ conformal model. This allows us to determine all three-point correlations involving the fields associated with the Potts order parameter and the energy density. The calculation uses screened Coulomb gas correlations. The Z₃ symmetry of the three-state Potts model is manifestly preserved.