International Journal of Modern Physics A

An analytical and nonperturbative approach to SU(2) and SU(3) Yang–Mills thermodynamics is developed and applied. Each theory comes in three phases: A deconfining, a preconfining, and a confining one. We show how macroscopic and inert scalar fields emerge in each phase and how they determine the ground-state physics and the properties of the excitations. While the excitations in the deconfining and preconfining phases are massless or massive gauge modes the excitations in the confining phase are massless or massive spin-1/2 fermions. The nature of the two phase transitions is investigated for each theory. We compute the temperature evolution of thermodynamical quantities in the deconfining and preconfining phase and estimate the density of states in the confining phase. Some implications for particle physics and cosmology are discussed.

The influence of dark matter (DM) on the growth of supermassive black holes (SMBHs) is studied. It is shown that gravitational scattering of DM particles on bulge stars leads to diffusion of DM in phase space {m, m_z, I} (m denotes the angular momentum and I is the radial action). Appropriate diffusion coefficients are calculated for different bulge models, and it is argued that the diffusion along m axis is the most important effect. It is shown that this process leads to noticeable flow of DM into the black hole (BH), resulting in its power-law growth: M_bh ∝ t^9/16. Comparison with observational data shows that, in principle, this effect may explain observed masses of SMBHs. Special attention is paid to the corrections related to the innermost region of BH gravitational influence and the diffusion along I axis. Their influence on the BH growth law is shown to be negligible.

We consider supersymmetric SO(10) grand unification where the unified gauge group can break to the Standard Model gauge group through different chains. The breaking of SO(10) necessarily involves the reduction of the rank, and consequent generation of nonuniversal supersymmetry breaking scalar mass terms. We derive squark and slepton mass relations, taking into account these nonuniversal contributions to the sfermion masses, which can help distinguish between the different chains through which the SO(10) gauge group breaks to the Standard Model gauge group. We then study some implications of these nonuniversal supersymmetry breaking scalar masses for the low energy phenomenology.

To describe the "slow" motions of n interacting mass points, we give the most general four-dimensional (4D) noninstantaneous, nonparticle symmetric Galilei-invariant variational principle. It involves two-body invariants constructed from particle 4-positions and 4-velocities of the proper orthochronous inhomogeneous Galilei group. The resulting 4D equations of motion and multiple-time conserved quantities involve integrals over the worldlines of the other n-1 interacting particles. For a particular time-asymmetric retarded (advanced) interaction, we show the vanishing of all integrals over worldlines in the ten standard 4D multiple-time conserved quantities, thus yielding a Newtonian-like initial value problem. This interaction gives 3D noninstantaneous, nonparticle symmetric, coupled nonlinear second-order delay-differential equations of motion that involve only algebraic combinations of nonsimultaneous particle positions, velocities, and accelerations. The ten 3D noninstantaneous, nonparticle symmetric conserved quantities involve only algebraic combinations of nonsimultaneous particle positions and velocities. A two-body example with a generalized Newtonian gravity is provided. We suggest that this formalism might be useful as an alternative slow-motion mechanics for astrophysical applications.

Recently, we have reported on the existence of some monopoles, multimonopole, and antimonopoles configurations. In this paper we would like to present more monopoles, multimonopole, and antimonopoles configurations of the magnetic ansatz of Ref. 9 when the parameters p and b of the solutions takes different serial values. These exact solutions are a different kind of BPS solution. They satisfy the first order Bogomol'nyi equation but possess infinite energy. They can have radial, axial, or rotational symmetry about the z-axis. We classified these serial solutions as (i) the multimonopole at the origin; (ii) the finitely separated 1-monopoles; (iii) the screening solutions of multimonopole and (iv) the axially symmetric monopole solutions. We also give a construction of their anticonfigurations with all the magnetic charges of poles in the configurations reversed. Half-integer topological magnetic charge multimonopole also exist in some of these series of solutions.

This paper is aimed to elaborate the problem of energy–momentum in general relativity. In this connection, we use the prescriptions of Einstein, Landau–Lifshitz, Papapetrou and Möller to compute the energy–momentum densities for two exact solutions of Einstein field equations. The space–times under consideration are the nonnull Einstein–Maxwell solutions and the singularity-free cosmological model. The electromagnetic generalization of the Gödel solution and the Gödel metric become special cases of the nonnull Einstein–Maxwell solutions. It turns out that these prescriptions do not provide consistent results for any of these space–times. These inconsistent results verify the well-known proposal that the idea of localization does not follow the lines of pseudotensorial construction but instead follows from the energy–momentum tensor itself. These differences can also be understood with the help of the Hamiltonian approach.

We consider a more general initial condition satisfying the minimal uncertainty relationship. We calculate the power spectrum of a simple model in inflationary cosmology. The results depend on perturbations generated below a fundamental scale, e.g. the Planck scale.

Recently a significant progress in matching the anomalous dimensions of certain class of operators in N = 4 SYM and rotating strings was made. The correspondence was established mainly by use of Bethe ansatz technique applied to the spin s Heisenberg chain model. In a recent paper,¹⁶ the author suggested to solve the Heisenberg model by use of sigma model approach. In this current work we generalize the solutions presented in Ref. 16 and comment on the dual string theory. It turns out that our solution is related to a generalized ansatz for rotating strings which can be reduced to the so-called Neumann–Rosochatius integrable system. We comment on the spin chain sigma model and string solutions and the possibilities for a more precise formulation of the string/gauge theory correspondence.

A new discrete Lax operator involving discrete canonical variable is introduced which generate new integrable system, and is analyzed in the light of the new concept of canonical Bäcklund transformation and classical r-matrix. The generating function of the transformation is explicitly deduced. The second half of the paper deals with the quantization problem where an explicit form of the Bethe equations are deduced.