Finite temperature Casimir effect in spacetime with extra compactified dimensions

In this Letter, we derive the explicit exact formulas for the finite temperature Casimir force acting on a pair of parallel plates in the presence of extra compactified dimensions within the framework of Kaluza–Klein theory. Using the piston analysis, we show that at any temperature, the Casimir force due to massless scalar field with Dirichlet boundary conditions on the plates is always attractive and the effect of extra dimensions becomes stronger when the size or number of the extra dimensions increases. These properties are not affected by the explicit geometry and topology of the Kaluza–Klein space.     

Finite temperature Casimir effect in Kaluza–Klein spacetime

In this article, we consider the finite temperature Casimir effect in Kaluza–Klein spacetime due the vacuum fluctuation of massless scalar field with Dirichlet boundary conditions. We consider the general case where the extra dimensions (internal space) can be any compact connected manifold or orbifold without boundaries. Using piston analysis, we show that the Casimir force is always attractive at any temperature, regardless of the geometry of the internal space. Moreover, the magnitude of the Casimir force increases as the size of the internal space increases and it reduces to the Casimir force in (3+1)$(3+1)$-dimensional Minkowski spacetime when the size of the internal space shrinks to zero. In the other extreme where the internal space is large, the Casimir force can increase beyond all bound. Asymptotic behaviors of the Casimir force in the low and high temperature regimes are derived and it is observed that the magnitude of the Casimir force grows linearly with temperature in the high temperature regime.     

Renormalization in theories with modified dispersion relations: Weak gravitational fields

We consider a free quantum scalar field satisfying modified dispersion relations in curved spacetimes, within the framework of Einstein–Aether theory. Using a power counting analysis, we study the divergences in the adiabatic expansion of 〈?²〉$〈{?}^2〉$ and 〈T_μν〉$〈T_{\mu \nu }〉$, working in the weak field approximation. We show that for dispersion relations containing up to 2s powers of the spatial momentum, the subtraction necessary to renormalize these two quantities on general backgrounds depends on s   in a qualitatively different way: while 〈?²〉$〈{?}^2〉$ becomes convergent for a sufficiently large value of s  , the number of divergent terms in the adiabatic expansion of 〈T_μν〉$〈T_{\mu \nu }〉$ increases with s. This property was not apparent in previous results for spatially homogeneous backgrounds.     

Generally covariant quantization and the Dirac field

Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of the corresponding quantum operators. The Dirac theory is investigated and it is shown that, in contrast to the case of bosonic fields, in curved spacetime, the field momentum does not coincide with the generators of spacetime translations. The reason is traced back to the presence of second class constraints occurring in Dirac theory. Further, it is shown that the modification of the Dirac Lagrangian by a surface term leads to a momentum transfer between the Dirac field and the gravitational background field, resulting in a theory that is free of constraints, but not manifestly hermitian.     

Vacuum Fluctuations and Motion of a Charged Test Particle in a Cylindrical Spacetime

The effects of quantum electromagnetic fluctuations upon the motion of a test charged particle are examined in a cylindrical spacetime in which one spatial is compactified. The mean squared fluctuations in the velocity and position of the test particle are calculated. It is found that the random motion of the test particle will be anisotropic. The possible consequences for theories with extra compactified spatial dimensions are discussed.     

Radiative corrections with 5D mixed position-/momentum-space propagators

In higher dimensional field theories with compactified dimensions there are three standard ways to do perturbative calculations: (i) by the summation over Kaluza-Klein towers; (ii) by the summation over winding numbers making use of the Poisson-resummation formula; and (iii) by using mixed propagators, where the coordinates of the four infinite dimensions are Fourier-transformed to momentum space while those of the compactified dimension are kept in configuration space. The third method is broadly used in finite temperature field theory calculations. One of its advantages is that one can easily separate the ultraviolet divergent terms of the uncompactified theory from the non-local finite corrections arising from windings around the compact dimensions. In this note we demonstrate the use of this formalism by calculating one-loop self-energy corrections in a 5D theory formulated on the manifold and on the orbifold .     

On the 4D effective theory in warped compactifications with fluxes and branes

We present a systematic way to derive the four-dimensional effective theories for warped compactifications with fluxes and branes in the ten-dimensional type IIB supergravity. The ten-dimensional equations of motion are solved using the gradient expansion method and the effective four-dimensional equations of motions are derived by imposing the consistency condition that the total derivative terms with respect to the six-dimensional internal coordinates vanish when integrated over the internal manifold. By solving the effective four-dimensional equations, we can find the gravitational backreaction to the warped geometry due to the dynamics of moduli fields, branes and fluxes.     

Dynamics of superhorizon photons during inflation with vacuum polarization

We study asymptotic dynamics of photons propagating in the polarized vacuum of a locally de Sitter Universe. The origin of the vacuum polarization is fluctuations of a massless, minimally coupled, scalar, which we model by the one-loop vacuum polarization tensor of scalar electrodynamics. We show that late time dynamics of the electric field on superhorizon scales approaches that of an Airy oscillator. The magnetic field amplitude, on the other hand, asymptotically approaches a nonvanishing constant (plus an exponentially small oscillatory component), which is suppressed with respect to the initial (vacuum) amplitude. This implies that the asymptotic photon dynamics is more intricate than that of a massive photon obeying the local Proca equation.     

Renormalization-group flow for the field strength in scalar self-interacting theories

We consider the renormalization-group coupled equations for the effective potential V(?)$V(?)$ and the field strength Z(?)$Z(?)$ in the spontaneously broken phase as a function of the infrared cutoff momentum k  . In the k→0$k\to 0$ limit, the numerical solution of the coupled equations, while consistent with the expected convexity property of V(?)$V(?)$, indicates a sharp peaking of Z(?)$Z(?)$ close to the end points of the flatness region that define the physical realization of the broken phase. This might represent further evidence in favor of the non-trivial vacuum field renormalization effect already discovered with variational methods.     

Coincidence problem in YM field dark energy model

The coincidence problem is studied in the effective Yang–Mills condensate dark energy model. As the effective YM Lagrangian is completely determined by quantum field theory, there is no adjustable parameter in this model except the energy scale, and the cosmic evolution only depends on the initial conditions. For generic initial conditions with the YM condensate subdominant to the radiation and matter, the model always has a tracking solution, the Universe transits from matter-dominated into the dark energy dominated stage only recently z∼0.3$z\sim 0.3$, and evolve to the present state with Ωy∼0.73${\Omega }_y\sim 0.73$ and Ωm∼0.27${\Omega }_m\sim 0.27$.     

Localising gravity in composite monopole brane worlds without bulk cosmological constant

We study a 7-dimensional brane world scenario with a Ricci-flat 3-brane residing in the core of a composite monopole defect, i.e., a defect composed of a 't Hooft–Polyakov and a global monopole. Admitting a direct interaction between the two bosonic sectors of the theory, we analyse the structure of the space–time in the limits of small, respectively large direct interaction coupling constant. For large direct interaction, the global monopole disappears from the system and leaves behind a negative cosmological constant in the bulk such that gravity-localising solutions are possible without a priori introduction of a bulk cosmological constant.     

Analytic approach to the thermal Casimir force between metal and dielectric

The analytic asymptotic expressions for the Casimir free energy, pressure and entropy at low temperature in the configuration of one metal and one dielectric plate are obtained. For this purpose we develop the perturbation theory in a small parameter proportional to the product of the separation between the plates and the temperature. This is done using both the simplified model of an ideal metal and of a dielectric with constant dielectric permittivity and for the realistic case of the metal and dielectric with frequency-dependent dielectric permittivities. The analytic expressions for all related physical quantities at high temperature are also provided. The obtained analytic results are compared with numerical computations and good agreement is found. We demonstrate for the first time that the Lifshitz theory, when applied to the configuration of metal-dielectric, satisfies the requirements of thermodynamics if the static dielectric permittivity of a dielectric plate is finite. If it is infinitely large, the Lifshitz formula is shown to violate the Nernst heat theorem. The implications of these results for the thermal quantum field theory in Matsubara formulation and for the recent measurements of the Casimir force between metal and semiconductor surfaces are discussed.     

Black hole thermodynamics and the factor of 2 problem

We show that the recent tunneling formulas for black hole radiation in static, spherically symmetric spacetimes follow as a consequence of the first law of black hole thermodynamics and the area-entropy relation based on the radiation temperature. A tunneling formula results even if the radiation temperature is different from the one originally derived by Hawking and this is discussed in the context of the recent factor of 2 problem. In particular, it is shown that if the radiation temperature is higher than the Hawking temperature by a factor of two, thermodynamics then leads to a tunneling formula which is exactly the one recently found to be canonically invariant.     

Phase transitions and perfectness of fluids in weakly coupled real scalar field theories

We calculate the ratio η/s$\eta /s$, the shear viscosity (η) to entropy density (s  ), which characterizes how perfect a fluid is, in weakly coupled real scalar field theories with different types of phase transitions. The mean-field results of the η/s$\eta /s$ behaviors agree with the empirical observations in atomic and molecular systems such as H₂O, He, N, and all the matters with data available in the NIST database. These behaviors are expected to be the same in N   component scalar theories with an O(N)$O(N)$ symmetry. We speculate these η/s$\eta /s$ behaviors are general properties of fluid shared by QCD and cold atoms. Finally, we clarify some issues regarding counterexamples of the conjectured universal bound η/s?1/4π$\eta /s?1/4\pi$ found in Refs. [T.D. Cohen, Phys. Rev. Lett. 99 (2007) 021602, hep-th/0702136; A. Cherman, T.D. Cohen, P.M. Hohler, arXiv: 0708.4201 [hep-th]; A. Dobado, F.J. Llanes-Estrada, Eur. Phys. J. C 51 (2007) 913, hep-th/0703132]     

Localization of nonlocal theories

We show that a certain class of nonlocal scalar models, with a kinetic operator inspired by string field theory, is equivalent to a system which is local in the coordinates but nonlocal in an auxiliary evolution variable. This system admits both Lagrangian and Hamiltonian formulations, and its Cauchy problem and quantization are well-defined. We classify exact nonperturbative solutions of the localized model which can be found via the diffusion equation governing the fields.     

On the formulation of D = 11 supergravity and the composite nature of its three-form gauge field

The underlying gauge group structure of the D = 11 Cremmer-Julia-Scherk supergravity becomes manifest when its three-form field A₃ is expressed through a set of one-form gauge fields, , , η_1α, and E^a, ψ^α. These are associated with the generators of the elements of a family of enlarged supersymmetry algebras parametrized by a real number s. We study in detail the composite structure of A₃ extending previous results by D’Auria and Fré, stress the equivalence of the above problem to the trivialization of a standard supersymmetry algebra E^(11|32) cohomology four-cocycle on the enlarged superalgebras, and discuss its possible dynamical consequences. To this aim we consider the properties of the first order supergravity action with a composite A₃ field and find the set of extra gauge symmetries that guarantee that the field theoretical degrees of freedom of the theory remain the same as with a fundamental A₃. The extra gauge symmetries are also present in the so-called rheonomic treatment of the first order D = 11 supergravity action when A₃ is composite. Our considerations on the composite structure of A₃ provide one more application of the idea that there exists an extended superspace coordinates/fields correspondence. They also suggest that there is a possible embedding of D = 11 supergravity into a theory defined on the enlarged superspace .     

Brane gravitational interactions from 6D supergravity

We investigate the massive graviton contributions to 4D gravity in a 6D brane world scenario, whose bulk field content can include that of 6D chiral gauged supergravity. We consider a general class of solutions having 3-branes, 4D Poincaré symmetry and axisymmetry in the internal space. We show that these contributions, which we compute analytically, can be independent of the brane vacuum energy as a consequence of geometrical and topological properties of the above-mentioned codimension two brane world. These results support the idea that in such models the gravitational interactions may be decoupled from the brane vacuum energy.     

Statistics in the landscape of intersecting brane models

An approach towards a statistical survey of four-dimensional supersymmetric vacua in the string theory landscape is described and illustrated with three examples of ensembles of intersecting D-brane models. The question whether it is conceivable to make predictions based on statistical distributions is discussed. Especially interesting in this context are possible correlations between low energy observables. As an example we look at correlations between properties of the gauge sector of intersecting D-brane models and Gepner model constructions. Based on a talk presented at “The 15th International Conference on Supersymmetry and the Unification of Fundamental Interactions”, July 26–August 1, 2007, Karlsruhe, Germany.