International Journal of Modern Physics A

The bosonic string theory evolved as an attempt to find a multidimensional analogue of Euler's beta function to describe the multiparticle Veneziano amplitudes. Such an analogue had in fact been known in mathematics at least in 1922. Its mathematical meaning was studied subsequently from different angles by mathematicians such as Selberg, Weil and Deligne among others. The mathematical interpretation of multidimensional beta function that was developed subsequently is markedly different from that described in physics literature. This paper aims to bridge the gap between the mathematical and physical treatments of such beta functions thus providing new topological, algebro-geometric, number-theoretic and combinatorial treatments of the multiparticle Veneziano and Veneziano-like amplitudes. As a result, the entirely new physical meaning of these amplitudes is emerging: they are periods connected with differential forms living on Fermat (hyper)surfaces. Such surfaces are considered as complex projective varieties of Hodge type. Obtained results allow to interpret the particle mass spectrum in terms of the Hodge spectrum of underlying Fermat (hyper)surface. The computational formalism although resembles that used in mirror symmetry calculations employs many additional results from topology, number theory, theory of singularities, etc. It allows to obtain the correlation functions in particle physics and conformal field theories using the same type of the Picard–Fuchs equations.

We discuss the generalization of the connection between the determinant of an operator entering a quadratic form and the associated Gaussian path-integral valid for Grassmann variables to the para-Grassmann case [θ^p+1=0 with p=1(p>1) for Grassmann (para-Grassmann) variables]. We show that the q-deformed commutation relations of the para-Grassmann variables lead naturally to consider q-deformed quadratic forms related to multiparametric deformations of GL(n) and their corresponding q-determinants. We suggest a possible application to the study of disordered systems.

In supersymmetry, there are gauge invariant dimension 5 proton decay operators which must be suppressed by a mass scale much larger than the Planck mass. It is natural to expect that this suppression should be explained by a mechanism that explains the hierarchical structure of the fermion mass matrices. We apply this argument to the case where wave functions of chiral multiplets are localized under a kink background along an extra spatial dimension and the Yukawa couplings as well as the coefficients of the proton decay operators are determined by the overlap of the relevant wave functions. A configuration is found in the context of SU(5) supersymmetric grand unified theory that yields realistic values of quark masses, mixing angles, CP phase and charged lepton masses and sufficiently small genuine dimension 5 proton decay operators. Inclusion of SU(5) breaking effects is essential in order to obtain non-vanishing CP phase as well as correct lepton masses. The resulting mass matrix has a texture structure in which texture zeros are a consequence of extremely small overlap of the wave functions. Our approach requires explicit breaking of supersymmetry in the extra dimension, which can be realized in (de)constructing extra dimension.

We consider the motion of relativistic particles described by an action that is linear in the torsion (second curvature) of the particle path. The Euler–Lagrange equations and the dynamical constants of the motion associated with the Poincaré group, the mass and the spin of the particle, are expressed in a simple way in terms of the curvatures of the embedded worldline. The moduli spaces of solutions are completely exhibited in four-dimensional background spaces and in the five-dimensional case we explicitly obtain the curvatures of the worldline.

We develop a systematic procedure for deriving canonical string field theory from large N matrix models in the Berenstein–Maldacena–Nastase limit. The approach, based on collective field theory, provides a generalization of the standard string field theory.

We calculate the mass spectrum, the splitting values and some other properties in the framework of the semirelativistic equation by applying the shifted large-N expansion technique. We use seven different central potentials together with an improved QCD-motivated interquark potentials calculated to two loops in the modified minimal-subtraction scheme. The parameters of these potentials are fitted to generate the semirelativistic bound states of quarkonium system in close conformity with the experimental and the present available calculated center-of-gravity (c.o.g.) data. Calculations of the energy bound states are carried out up to third order. Our results are in excellent fit with the results of the other works.

I present a unified approach to calculating the next-to-next-to-leading order (NNLO) soft and virtual QCD corrections to cross-sections for electroweak, Higgs, QCD, and SUSY processes. I derive master formulas that can be used for any of these processes in hadron–hadron and lepton–hadron collisions. The formulas are based on a unified threshold resummation formalism and can be applied to both total and differential cross-sections for processes with either simple or complex color flows and for various factorization schemes and kinematics. As a test of the formalism, I rederive known NNLO results for Drell–Yan and Higgs production, deep inelastic scattering, and W⁺γ production, and I obtain expressions for several two-loop anomalous dimensions and other quantities needed in next-to-next-to-leading-logarithm (NNLL) resummations. I also present new results for the production of supersymmetric charged Higgs bosons; massive electroweak vector bosons; photons; heavy quarks in lepton–hadron and hadron–hadron collisions and in flavor-changing neutral current processes; jets; and squarks and gluinos. The NNLO soft and virtual corrections are often dominant, especially near threshold, and they reduce the scale dependence of the cross-section. Thus, a unified approach to these corrections is important in the search for new physics at present and future colliders.

It is a well-known result that the scalar field is composed of two chiral particles (Floreanini–Jackiw particles) of opposite chiralities. Also, that a Siegel particle spectrum is formed by a nonmover field (a Hull's noton) and a FJ particle. In this work, we show that in a scalar field spectrum, in a curved expanding universe scenario, we find a different result, two dynamical chiral fields.