International Journal of Modern Physics A

Curvature and torsion are the two tensors characterizing a general Riemannian space–time. In Einstein's general theory of gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the curvature tensor plays the central role. For such a purely metric geometry, two well-known topological invariants, namely the Euler class and the Pontryagin class, are useful in characterizing the topological properties of the space–time. From a gauge theory point of view, and especially in the presence of spin, torsion naturally comes into play, and the underlying space–time is no longer purely metric. We describe a torsional topological invariant, discovered in 1982, that has now found increasing usefulness in recent developments.

The running mass of the b-quark defined in -scheme is one of the important parameters of SUSY QCD. To find its value, it should be related to some known experimental input. In this paper, the b-quark running mass defined in nonsupersymmetric QCD is chosen for determination of the corresponding parameter in SUSY QCD. The relation between these two quantities is found by considering five-flavor QCD as an effective theory obtained from its supersymmetric extension. A numerical analysis of the calculated two-loop relation and its impact on the MSSM spectrum is discussed. Since for nonsupersymmetric models -scheme is more natural than , we also propose a new procedure that allows one to calculate relations between - and -parameters. Unphysical ε-scalars that give rise to the difference between the above-mentioned schemes are assumed to be heavy and decoupled in the same way as physical degrees of freedom. By means of this method it is possible to "catch two rabbits," i.e. decouple heavy particles and turn from to , at the same time. An explicit two-loop example of transition is given in the context of QCD. The advantages and disadvantages of the method are briefly discussed.

We construct a quantum theory of free fermion field based on the deformed Heisenberg algebra where β is a deformation parameter using supersymmetry as a guiding principle. A supersymmetric field theory with a real scalar field and a Majorana fermion field is given explicitly and we also find that the supersymmetry algebra is deformed from an usual one.

We evaluate the ground state degeneracy of noncommutative Chern–Simons models on the two-torus, a quantity that is interpreted as the "topological order" of associated phases of Hall fluids. We define the noncommutative theory via T-duality from an ordinary Chern–Simons model with non-Abelian 't Hooft magnetic fluxes. Motivated by this T-duality, we propose a discrete family of noncommutative, non-Abelian fluid models, arising as a natural generalization of the standard noncommutative Chern–Simons effective models. We compute the topological order for these universality classes, and comment on their possible microscopic interpretation.

We study the hierarchy of hidden space–time symmetries of noncritical strings in RNS formalism, realized nonlinearly. Under these symmetry transformations the variation of the matter part of the RNS action is canceled by that of the ghost part. These symmetries, referred to as the α-symmetries, are induced by special space–time generators, violating the equivalence of ghost pictures. We classify the α-symmetry generators in terms of superconformal ghost cohomologies H_n ~ H_-n-2(n≥0) and associate these generators with a chain of hidden space–time dimensions, with each ghost cohomology H_n ~ H_-n-2 "contributing" an extra dimension. Namely, we show that each ghost cohomology H_n ~ H_-n-2 of noncritical superstring theory in d-dimensions contains d+n+1 α-symmetry generators and the generators from H_k ~ H_-k-2, 1≤k ≤n, combined together, extend the space–time isometry group from the naive SO(d, 2) to SO(d+n, 2). In the simplest case of n = 1 the α-generators are identified with the extra symmetries of the 2T-physics formalism, also known to originate from a hidden space–time dimension.

We study the bridge between the phenomenological mass matrix model and SO(10) GUT. Namely, we consider the four-zero texture model in the framework of the renormalizable SO(10) GUT model. This unification gives more stringent constraints than the case where only either model is considered. However, we can obtain good fitting by expanding the minimal SO(10) GUT to include 120 in addition to 10 and in Yukawa coupling and by considering both type I and type II seesaw mechanisms.

We derive the spectrum in the broken phase of a λϕ⁴ theory, in the limit λ→∞, showing that this goes as even integers of a renormalized mass in agreement with recent lattice computations.

In this paper, we formulate a planar limited version of the B-side in homological mirror symmetry that formularizes Chern–Simons-type topological open string field theory using homotopy associative algebra (A_∞ algebra). This formulation is based on the works by Dijkgraaf and Vafa. We show that our formularization includes gravity/gauge theory correspondence which originates in the AdS/CFT duality of Dijkgraaf–Vafa theory.

We consider in this paper φ⁴ theory in higher dimensions. Using functional diagrammatic approach, we compute the one-loop correction to effective potential of the scalar field in five dimensions. It is shown that φ⁴ theory can be regularized in five dimensions. Temperature dependent one-loop correction and critical temperature β_c are computed and β_c depends on the fundamental scale of the theory. A brief discussion of symmetry restoration is also presented. The nature of phase transitions is examined and is of second order.

In this paper we use ΔP = -1.772341 ± 13.153788 s between the phenomenologically determined orbital period P_b of the PSR J0737-3039A/B double pulsar system and the purely Keplerian period calculated with the system's parameters, determined independently of the third Kepler law itself, in order to put constraints on some models of modified gravity (f(R), Yukawa-like fifth force, MOND). The major source of error affecting ΔP is not the one in the phenomenologically measured period (δP_b = 4×10^-6s), but the systematic uncertainty δP⁽⁰⁾ in the computed Keplerian one due to the relative semimajor axis a mainly caused, in turn, by the errors in the ratio of the pulsars' masses and in sin i. We get |κ| ≤ 0.8 × 10^-26m^-2 for the parameter that in the f(R) framework is a measure of the nonlinearity of the theory, |α| ≤ 5.5 × 10^-4 for the fifth-force strength parameter (for λ ≈ a = 0.006 AU). The effects predicted by the strong-acceleration regime of MOND are far too small to be constrained with some effectiveness today and in the future as well. In view of the continuous timing of such an important system, it might happen that in the near future it will be possible to obtain somewhat tighter constraints.

The Newtonian gravitational constant has still 150 parts per million of uncertainty. This paper examines the linear and nonlinear equations governing the rotational dynamics of the torsion gravitational balance. A nonlinear effect modifying the oscillation period of the torsion gravitational balance is carefully explored.

We discuss the low-mass enhancement effect in the baryon–antibaryon invariant mass in three-body baryonic B decays using final state interactions in the framework of Regge theory. We show that the rescattering between baryonic pair can reproduce the observed mass spectrum.