International Journal of Modern Physics A

Following a previous work on 2-dimensional Abelian (2,0)-gauge theories, one reacesses the analysis of the consistency of the dynamics of (2,0) "relaxed" Yang-Mills super-potentials and their coupling to (2,0)-nonlinear σ-model, by gauging the isotropy or the isometry group of the latter. One pays special attention to the extra "chiral-like" component-field gauge potential that comes out from the relaxation of superspace constraints.

We calculate the holographic conformal anomaly and brane Newton potential when bulk is 5d ads black hole. It is shown that such anomaly is the same as in the case of pure ads or (asymptotically) ds bulk spaces, i.e. it is (bulk) metric independent one. While Newton potential on the static brane in ads bh is different from the one in pure ads space, the gravity trapping still occurs for two branes systems. This indicates to metric independence of gravity localization.

A synthetic report of the advances in the study of classical and quantum string dynamics in curved backgrounds is provided, namely : the new feature of Multistring solutions; the mass spectrum of Strings in Curved backgrounds; The effect of a Cosmological Constant and of Spacial Curvature on Classical and Quantum Strings; Classical splitting of Fundamental Strings; The General String Evolution in constant Curvature Spacetimes; The Conformal Invariance Effects; Strings on plane fronted and gravitational shock waves, string falling on spacetime singularities and its spectrum.

New Developments in String Gravity and String Cosmology are reported: String driven cosmology and its Predictions; The primordial gravitational wave background; Non-singular string cosmologies from Exact Conformal Field Theories; Quantum Field Theory, String Temperature and the String Phase of de Sitter space-time; Hawking Radiation in String Theory and the String Phase of Black Holes; New Dual Relation between Quantum Field Theory regime and String regime and the "QFT/String Tango"; New Coherent String States and Minimal Uncertainty Principle in string theory.

We present the result concerning the perturbative computation of the scattering process 1 + 2 → 1′ + 2′ up to second order in the coupling constant. This was obtained in the context of a deformed quantum field theory which is interpreted as a phenomenological theory describing the scattering of spin-0 composite particles.

Peierls brackets are part of the space-time approach to quantum field theory, and provide a Poisson bracket which, being defined for pairs of observables which are group invariant, is group invariant by construction. It is therefore well suited for combining the use of Poisson brackets and the full diffeomorphism group in general relativity. The present paper provides an introduction to the topic, with applications to gauge field theory.

We study gauge theories based on abelian p- forms on real compact hyperbolic manifolds. The tensor kernel trace formula and the spectral functions associated with free generalized gauge fields are analyzed.

We analyze the nonrelativistic quantum scattering problem of a charged particle by an Abelian magnetic monopole in the background of a global monopole. In addition to the magnetic and geometric effects, we consider the influence of the electrostatic self-interaction on the charged particle. Moreover, for the specific case where the electrostatic self-interaction becomes attractive, charged particle-monopole bound system can be formed and the respective energy spectrum is hydrogen-like one.

Starting with the topological classification of gauge fields on the sphere (Dirac monopoles) and of Higgs vacuum configurations (through the second homotopy group of the space of vacuum states), the features of minimum energy solutions to gauge theories with spontaneous symmetry breaking and in the presence of singularities (monopoles) are deduced. For each theory, this analysis reveals whether a monopole can exist isolated or must be attached to a massive string and how its flux must be distributed.

A general expression for the vacuum expectation values of some physical observables as well as their relative variances are derived by means of zeta function regularisation.

This work is a pedagogical account on the diagnosis of certain pathologies which arise when standard canonical quantization procedures are improperly used in the context of non globally hyperbolic spacetimes. The improper use of "helical times" to implement quantization is also addressed.

We present a reduction procedure to the so-called canonical form for the Euler-Lagrange equations of a general gauge theory. The reduction procedure reveals constraints in the Lagrangian formulation of singular theories and, in that respect, is similar to the Dirac procedure in the Hamiltonian formulation. Moreover, the reduction procedure allows one to reveal the gauge identities between the Euler-Lagrange equations. As a demonstration we apply the reduction procedure to theories without higher derivatives.

We review some generalizations of 't Hooft and Mandelstam ideas on confinement for theories with non-Abelian unbroken gauge groups.

In this work we compute the vacuum expectation values of the energy-momentum tensor and the average value of a massive, charged scalar field in the presence of a magnetic flux cosmic string for both zero- and finite-temperature cases.

The quantization of a scalar field in Ads leads to two kinds of normalizable modes, usually called regular and irregular modes. The regular one is easily taken into account in the standard prescription for the AdS/CFT correspondence. The irregular mode requires a modified prescription which argue is not completely satisfactory. We discuss an alternative quantization in AdS which incorporates boundary terms in a natural way. Within this quantization scheme we present an improved prescription for the AdS/CFT correspondence which can be applied to both, regular and irregular modes. Boundary conditions other than Dirichlet are naturally treated in this new improved setting.

In this work we explain the construction of the thermal vacuum for the bosonic string, as well that of the thermal boundary state interpreted as a D_p-brane at finite temperature. In both case we calculate the respective entropy using the entropy operator of the Thermo Field Dynamics theory. We show that the contribution of the thermal string entropy is explicitly present in the D_p-brane entropy. Furthermore, we show that the Thermo Field approach is suitable to introduce temperature in boundary states.

Witten's observables of topological Yang-Mills theory, defined as classes of an equivariant cohomology, are re-obtained as the BRST cohomology classes of a superspace version of the theory.

In this contribution the tree-level effective actions for gluons and gravitons, as derived from Open and Closed Superstring theories, are reviewed respectively. As known for a long time, at zero order in α′ (the string fundamental constant) the first action is pure Yang-Mills while the second one is pure Einstein-Hilbert. The first Superstring Theory corrections turn up to appear at order in the first case while they appear at in the second one, as known from the three and four-point scattering amplitudes for gluons and gravitons, respectively. Recent work involving the order contributions to the Yang-Mills action is reviewed with some detail, including the authors' present line of research. Also, the uncharted territory of five graviton scattering is commented, looking forward to derive the Superstring Theory corrections to the Einstein-Hilbert action.

It is shown that besides the standard real algebraic framework for M-theory a consistent octonionic realization can be introduced. The octonionic M-superalgebra and superconformal M-algebra are derived. The first one involves 52 real bosonic generators and presents a novel and surprising feature, its octonionic M5 (super-5-brane) sector coincides with the M1 and M2 sectors. The octonionic superconformal M-algebra is given by OS_p(1,8∣O) and admits 239 bosonic and 64 fermionic generators.

The holographic principle in a radiation dominated universe is extended to incorporate the case of a bulk-viscous cosmic fluid. This corresponds to a nonconformally invariant theory. Generalization of the Cardy-Verlinde entropy formula to the viscous case appears to be possible from a formal point of view, although we question on physical grounds the manner in which the Casimir energy is evaluated in this case. Also, we consider in the present paper an observation recently made by Youm, namely that the entropy of the universe is no longer expressible in the conventional Cardy-Verlinde form if one relaxes the radiation dominance equation of state and instead merely assumes that the pressure is proportional to the energy density. We show that Youm's generalized entropy formula remains valid when the cosmic fluid is no longer ideal, but endowed with a constant bulk viscosity ζ.

It is discussed that the Ernst–Schwarzschild metric describing a nonrotating black hole in the external magnetic field admits the solutions of the Dirac monopole types for the corresponding Maxwell equations. The given solutions are obtained in explicit form and a possible influence of the conforming Dirac monopoles on Hawking radiation is also outlined.

The effect of the exponential pair creation from vacuum by the external field periodic in time is discussed. Two prospective applications of this physical effect in quantum field theory and in inflationary cosmology are considered. Being a nontrivial example of a parametric resonance, the effect of exponential pair creation may serve as an illustration of the effectiveness of mathematics in physical theory.

After a short presentation of KMS states and modular theory as the unifying description of thermalizing systems we propose the absence of transverse vacuum fluctuations in the holographic projections as the principle reason for an area behavior (the transverse area) of localization entropy as opposed to the volume dependence of ordinary heat bath entropy. Thermalization through causal localization is not a property of QM but results from the omnipresent vacuum polarization in QFT and does not require a Gibbs type ensemble avaraging (coupling to a heat bath).

The global multiplicative properties of Laplace type operators acting on irreducible rank one symmetric spaces are considered. The explicit form of the multiplicative anomaly is derived and its corresponding value is calculated exactly, for important classes of locally symmetric spaces and different dimensions.

We comment on some apparently weak points in the novel strategies recently developed by various authors aiming at a proof of the Riemann hypothesis. After noting the existence of relevant previous papers where similar tools have been used, we refine some of these strategies. It is not clear at the moment if the problems we point out here can be resolved rigorously, and thus a proof of the RH be obtained, along the lines proposed. However, a specific suggestion of a procedure to overcome the encountered difficulties is made, what constitutes a step towards this goal.

For positive elliptic differential operators Δ, the asymptotic expansion of the heat trace tr(e^-tΔ) and its related zeta function ζ(s, Δ) = tr(Δ^-s) have numerous applications in geometry and physics. This article discusses the general nature of the boundary conditions that must be considered when there is a singular stratum, and presents three examples in which a choice of boundary conditions at the singularity must be made. The first example concerns the signature operator on a manifold with a singular stratum of conic type. The second concerns the "Zaremba problem" for a nonsingular manifold with smooth boundary, posing Dirichlet conditions on part of the boundary and Neumann conditions on the complement; the intersection of these two regions can be viewed as a singular stratum of conic type, and a boundary condition must be imposed along this stratum. The third example is a one-dimensional manifold where the operator at one end has a singularity like that in conic problems, and the choice of boundary conditions affects not just the residues at the poles of the zeta function, but also the very location of the poles

For the three-dimensional BTZ black hole we consider a Selberg type zeta function. We indicate how special values of its logarithm correspond to certain thermodynamic quantities associated with the black hole.

We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1 < h < 2, a fractal distribution function associated with a fractal von Newmann entropy. Fractons are charge-flux systems defined in two-dimensional multiply connected space and they carry rational or irrational values of spin. This formulation can be considered in the context of the fractional quantum Hall effect-FQHE and number theory.

The time evolution of ionic internal states for trapped cold ions interacting with external laser in a harmonic oscillator potential, and a potential with a small nonlinear component varying as x⁶, modeled through a q-deformed harmonic oscillator, is briefly discussed. The entanglement of ionic internal states and center of mass vibrational states results in collapse and revival of population inversion. For deformation parameter, τ = 0.004(q = e^τ), the population inversion shows an extremely well behaved collapse and revival pattern. Next a simple application where entanglement is used for implementing quantum logic gates with ion trap placed inside an optical cavity, is presented. It is found that faster ionic state manipulation times can be obtained by working beyond the Lamb-Dicke regime.