We investigate the Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor for a scalar field with general curvature coupling parameter in $(D+1)$-dimensional de Sitter spacetime with an arbitrary number of compactified spatial dimensions. Both cases of periodicity and antiperiodicity conditions along the compactified dimensions are considered. Recurrence formulae are derived which express the vacuum expectation values for the dS spacetime of topology $\mathrm{R}^{p}\times (\mathrm{S}^{1})^{q}$ in the form of the sum of the vacuum expectation values in the topology $\mathrm{R}^{p+1}\times (\mathrm{S}^{1})^{q-1}$ and the part induced by the compactness of the $(p+1)$th spatial dimension. The behavior of the topological parts is investigated in various asymptotic regions of the parameters. In the early stages of the cosmological evolution the topological parts dominate the contribution in the expectation values due to the uncompactified dS part. In this limit the behavior of the topological parts does not depend on the curvature coupling parameter and coincides with that for a conformally coupled massless field. At late stages of the cosmological expansion the expectation values are dominated by the part corresponding to uncompactified dS spacetime. The vanishing of the topological parts is monotonic or oscillatory in dependence of the mass and the curvature coupling parameter of the field.
We present duality invariant structure of the thermodynamic quantities of non-extreme black hole solutions of torodially compactified Type II (M-theory) and heterotic string in five and four dimensions. These quantities are parameterized by duality invariant combinations of charges and the non-extremality parameter, which measures a deviation from the BPS-saturated limit. In particular, in D=5 we find explicit S- and T-duality [U-duality] invariant expressions for solutions of toroidally compactified heterotic string [Type II string]. In D=4, we consider general S-duality invariant expressions…
We investigate the fermionic condensate and the vacuum expectation values of the energy-momentum tensor for a massive spinor field in de Sitter spacetime with spatial topology $\mathrm{R}^{p}\times (\mathrm{S}^{1})^{q}$. Both cases of periodicity and antiperiodicity conditions along the compactified dimensions are considered. By using the Abel-Plana formula, the topological parts are explicitly extracted from the vacuum expectation values. In this way the renormalization is reduced to the renormalization procedure in uncompactified de Sitter spacetime. It is shown that in the uncompactified su…
We review the macroscopic and microscopic properties of black holes of toroidally compactified heterotic and Type II string theory in dimensions 4<=D<=9. General charged rotating black hole solutions are obtained by acting on a generating solution with classical duality symmetries. In D=4, D=5 and 6<=D<=9, the generating solution for both toroidally compactified Type II and heterotic strings is specified by the ADM mass, [(D-1)/2]-angular momentum components and five, three and two charges, respectively. We give the Bekenstein-Hawking entropy for these solutions, address the BPS-saturated limi…
It has been shown recently that the toroidally compactified type IIB string effective action possesses an SL(2, R) invariance as a consequence of the corresponding symmetry in ten dimensions when the self-dual five-form field strength is set to zero. By working in the string frame we clarify how a Z$_2$ subgroup of this SL(2, R) group responsible for producing the strong-weak coupling duality in the ten dimensional theory produces the same symmetry for the reduced theory. In the absence of the full covariant action of type IIB supergravity theory, we show that the T-dual version of type IIA st…
Vacuum energy density and stresses are investigated for a scalar field with general curvature coupling parameter in (D+1)-dimensional de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions. The corresponding expectation values are presented in the form of the sum of the vacuum expectation values in uncompactified dS spacetime and the part induced by the non-trivial topology. In the early stages of the cosmological evolution the topological parts dominate. In this limit the behavior of the Casimir densities does not depend on the curvature coupling parameter …
We present the most general rotating black hole solution of five-dimensional N=4 superstring vacua that conforms to the ``no hair theorem''. It is chosen to be parameterized in terms of massless fields of the toroidally compactified heterotic string. The solutions are obtained by performing a subset of O(8,24) transformations, i.e., symmetry transformations of the effective three-dimensional action for stationary solutions, on the five-dimensional (neutral) rotating solution parameterized by the mass m and two rotational parameters $l_1$ and $l_2$. The explicit form of the generating solution …
Fermionic condensate and the vacuum expectation values of the energy-momentum tensor are investigated for a massive spinor fields in higher-dimensional spacetimes with an arbitrary number of toroidally compactified spatial dimensions. By using the Abel-Plana summation formula and the zeta function technique we present the vacuum expectation values in two different forms. Applications of the general formulae to cylindrical and toroidal carbon nanotubes are given. We show that the topological Casimir energy is positive for metallic cylindrical nanotubes and is negative for semiconducting ones. T…
Toroidally compactified Yang-Mills theory on the lattice is studied by using the Hybrid Monte Carlo algorithm. When the compact dimensions are small, the theory naturally reduces to Yang-Mills with scalars. We confirm previous analytical and numerical results for pure gauge theory with scalars in (0+1) dimensions and at high temperatures to Super-Yang-Mills in (1+1) dimensions. In (1+1) dimensions, our simulations confirm the previously conjectured phase diagram. Furthermore, we find evidence for the sequential breaking of the center symmetry in (1+1) dimensions as a function of the volume. In…
The vacuum expectation value of the fermionic current is evaluated for a massive spinor field in spacetimes with an arbitrary number of toroidally compactified spatial dimensions in presence of a constant gauge field. By using the Abel-Plana type summation formula and the zeta function technique we present the fermionic current in two different forms. Non-trivial topology of the background spacetime leads to the Aharonov-Bohm effect on the fermionic current induced by the gauge field. The current is a periodic function of the magnetic flux with the period equal to the flux quantum. In the abse…
We address the issue of T-duality and U-duality symmetries in the toroidally-compactified type IIA string. It is customary to take as a starting point the dimensionally-reduced maximal supergravity theories, with certain field strengths dualised such that the classical theory exhibits a global $E_{n(n)}$ symmetry, where n=11-D in D dimensions. A discrete subgroup then becomes the conjectured U-duality group. In dimensions D\le 6, these necessary dualisations include NS-NS fields, whose potentials, rather than merely their field strengths, appear explicitly in the couplings to the string worlds…
We review exact results obtained for R^4 couplings in maximally supersymmetric type II string theories. These couplings offer a privileged scene to understand the rules of semiclassical calculus in string theory. Upon expansion in weak string coupling, they reveal an infinite sum of non-perturbative e^{-1/g} effects that can be imputed to euclidean D-branes wrapped on cycles of the compactification manifolds. They also shed light on the relation between Dp-branes and D-(p-2)branes, D-strings and (p,q) strings, instanton sums and soliton loops. The latter interpretation takes over in D<=6 in or…
We construct generating solutions for general D-dimensional ($4 \le D \le 9$) rotating, electrically charged, black holes in the effective action of toroidally compactified heterotic (or Type IIA) string. The generating solution is parameterized by the ADM mass, two electric charges and $[{D-1}\over 2]$ angular momenta (as well as the asymptotic values of one toroidal modulus and the dilaton field). For $D \ge 6$, those are generating solutions for {\it general} black holes in toroidally compactified heterotic (or type IIA) string. Since in the BPS-limit (extreme limit) these solutions have si…
In a recent paper we have given the macroscopic and microscopic description of the generating solution of toroidally compactified string theory BPS black holes. In this note we compute its corresponding microscopic entropy. Since by definition the generating solution is the most general solution modulo U-duality transformations, this result allows for a description of the fundamental degrees of freedom accounting for the entropy of any regular BPS black holes of toroidally compactified string (or M) theory.
In this paper, we analyze the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor associated with a charged and massive scalar quantum field in a generalized $(D+1)$-dimensional anti-de Sitter space in the presence of a cosmic string, admitting a magnetic flux running along the string's core. In addition we admit that an extra coordinate is compactified to a circle and presents a magnetic flux running along its center. This compactification is implemented by imposing a quasiperiodic condition on the field with an arbitrary phase. The calculation of the VEVs of …
Massless BPS-saturated states in toroidally compactified heterotic string were discussed first. Then, I constructed a large class of BPS-saturated states of toroidally compactified type II string theories. They were parametrized by four independent parameters. Both orthogonal and non-orthogonal intersections of non-perturbative states in the corresponding ten dimensional theories were discussed. Phenomenologically, I considered the string effect in the form of threshold corrections on dilatonic charged black holes, and the superpotential of N=1 supergravity theory
Using the heterotic--type II duality of $N=2$ string vacua in four space-time dimensions we study non-perturbative couplings of toroidally compactified six-dimensional heterotic vacua. In particular, the heterotic--heterotic $S$-duality and the Coulomb branch of tensor multiplets observed in six dimensions are studied from a four-dimensional point of view. We explicitly compute the couplings of the vector multiplets of several type II vacua and investigate the implications for their heterotic duals.
A new method for computing exact conformal partial wave expansions is developed and applied to approach the problem of Hilbert space (Wightman) positivity in a non-perturbative four-dimensional quantum field theory model. The model is based on the assumption of global conformal invariance on compactified Minkowski space. Bilocal fields arising in the harmonic decomposition of the operator product expansion prove to be a powerful instrument in exploring the field content. In particular, in the theory of a field of dimension 4 which has the properties of a (gauge invariant) Lagrangian, the scala…
We investigate T-duality of toroidally compactified Matrix model with arbitrary Ramond-Ramond backgrounds in the framework of noncommutative super Yang-Mills gauge theory.
Rationality of the Wightman functions is proven to follow from energy positivity, locality and a natural condition of global conformal invariance (GCI) in any number D of space-time dimensions. The GCI condition allows to treat correlation functions as generalized sections of a vector bundle over the compactification of Minkowski space and yields a strong form of locality valid for all non-isotropic intervals if assumed true for space-like separations.
We construct a new extreme black hole solution in toroidally compactified heterotic string theory. The black hole saturates the Bogomol'nyi bound, has zero angular momentum, but nonzero electric dipole moment. It is obtained by starting with a higher dimensional rotating charged black hole, and compactifying one direction in the plane of rotation.
Wightman function and vacuum expectation value of the field square are evaluated for a massive scalar field with general curvature coupling parameter subject to Robin boundary conditions on two codimension one parallel branes located on $(D+1)$-dimensional background spacetime $AdS_{D_1+1}\times Σ$ with a warped internal space $Σ$. The general case of different Robin coefficients on separate branes is considered. The application of the generalized Abel-Plana formula for the series over zeros of combinations of cylinder functions allows us to extract manifestly the part due to the bulk without …
The vacuum expectation value of the current density for a charged scalar field is investigated in Rindler spacetime with a part of spatial dimensions compactified to a torus. It is assumed that the field is prepared in the Fulling-Rindler vacuum state. For general values of the phases in the periodicity conditions and the lengths of compact dimensions, the expressions are provided for the Hadamard function and vacuum currents. The current density along compact dimensions is a periodic function of the magnetic flux enclosed by those dimensions and vanishes on the Rindler horizon. The obtained r…
Generators for the discrete U-duality groups of toroidally compactified M-theory in d>3 are presented and used to determine the d=3 U-duality group. This contribution summarizes the results of hep-th/9909150.
The D-brane spectrum of a class of $\Zop_2$ orbifolds of toroidally compactified Type IIA and Type IIB string theory is analysed systematically. The corresponding K-theory groups are determined and complete agreement is found. The charge densities of the various branes are also calculated.
The Casimir densities are investigated for a massive spinor field in de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions. The vacuum expectation value of the energy-momentum tensor is presented in the form of the sum of corresponding quantity in the uncompactified de Sitter spacetime and the part induced by the non-trivial topology. The latter is finite and the renormalization is needed for the first part only. The asymptotic behavior of the topological term is investigated in the early and late stages of the cosmological expansion. When the comoving leng…
We present dyonic multi-membrane solutions of the N=2 D=8 supergravity theory that serves as the effective field theory of the $T^2$-compactified type II superstring theory. The `electric' charge is fractional for generic asymptotic values of an axion field, as for D=4 dyons. These membrane solutions are supersymmetric, saturate a Bogomolnyi bound, fill out orbits of an $Sl(2;\Z)$ subgroup of the type II D=8 T-duality group, and are non-singular when considered as solutions of $T^3$-compactified D=11 supergravity. On $K_3$ compactification to D=4, the conjectured type II/heterotic equivalence …
We investigate the Wightman function, the vacuum expectation values of the field squared and the energy-momentum tensor for a massive scalar field with general curvature coupling in the generalized cosmic string geometry with a compact dimension along its axis. The boundary condition along the compactified dimension is taken in general form with an arbitrary phase. The vacuum expectation values are decomposed into two parts. The first one corresponds to the uncompactified cosmic string geometry and the second one is the correction induced by the compactification. The asymptotic behavior of the…
Vacuum energy density and stresses are investigated for a scalar field in de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions and in anti-de Sitter spacetime with two parallel branes. On the branes the field obeys the Robin boundary conditions. The behavior of the vacuum expectation values is discussed in various asymptotic regions of the parameters. Applications are given to Randall-Sundrum type braneworlds.
Fermionic condensate and the vacuum expectation values of the energy-momentum tensor are investigated for twisted and untwisted massive spinor fields in higher-dimensional de Sitter spacetime with toroidally compactified spatial dimensions. The expectation values are presented in the form of the sum of corresponding quantities in the uncompactified de Sitter spacetime and the parts induced by non-trivial topology. The latter are finite and the renormalization is needed for the first parts only. Closed formulae are derived for the renormalized fermionic vacuum densities in uncompactified odd-di…
The main objective of this paper is to analyze the vacuum expectation value (VEV) of the energy-momentum tensor (EMT) associated with a charged scalar quantum field in a high-dimensional cosmic string spacetime admitting the presence of a magnetic flux running along the string's core. In addition, we also assume that the coordinate along the string's axis is compactified to a circle and presents an extra magnetic flux running along its center. This compactification is implemented by imposing a quasiperiodic condition on the field with an arbitrary phase $β$. The calculation of the VEV of the E…
This paper explores the moduli-dependent coefficients of higher derivative interactions that appear in the low-energy expansion of the four-graviton amplitude of maximally supersymmetric string theory compactified on a d-torus. These automorphic functions are determined for terms up to order D^6R^4 and various values of d by imposing a variety of consistency conditions. They satisfy Laplace eigenvalue equations with or without source terms, whose solutions are given in terms of Eisenstein series, or more general automorphic functions, for certain parabolic subgroups of the relevant U-duality g…
We obtain extremal stationary solutions that generalize the Israel-Wilson-Perjés class for the low-energy limit of heterotic string theory with n>=3 U(1) gauge fields toroidally compactified from five to three dimensions. A dyonic solution is obtained using the matrix Ernst potential (MEP) formulation and expressed in terms of a single real 3X3-matrix harmonic function. By studying the asymptotic behaviour of the field configurations we define the physical charges of the field system. The extremality condition makes the charges to saturate the Bogomol'nyi-Prasad-Sommerfield (BPS) bound.
We investigate the vacuum expectation values of the field squared and the energy-momentum tensor for a massless scalar field with general curvature coupling parameter in spatially flat Friedmann-Robertson-Walker universes with an arbitrary number of toroidally compactified dimensions. When the comoving lengths of the compact dimensions are short compared to the Hubble length, the topological parts coincide with those for a conformal coupling. This limit corresponds to the adiabatic approximation. In the opposite limit of large comoving lengths of the compact dimensions, in dependence of the cu…
We investigate the Wightman function, the vacuum expectation values of the field squared and the energy-momentum tensor for a massless scalar field with general curvature coupling parameter in spatially flat Friedmann-Robertson-Walker universes with an arbitrary number of toroidally compactified dimensions. The topological parts in the expectation values are explicitly extracted and in this way the renormalization is reduced to that for the model with trivial topology. In the limit when the comoving lengths of the compact dimensions are very short compared to the Hubble length, the topological…
Double Field Theory (DFT) is a low-energy effective theory of a manifestly $O(D,D)$ invariant formulation of the closed string theory when toroidally compactified dimensions are present. The theory is based on a doubled spacetime structure and, in order to preserve the gauge symmetry provided by the invariance under generalized diffeomorphisms, a constraint has to be imposed on fields and gauge parameters. In this paper, we propose a DFT-inspired Supergravity by using a suitable {\em star product} that implements such constraint and the corresponding algebraic structure is explored. We get a c…
We investigate the finite temperature fermionic condensate and the expectation values of the charge and current densities for a massive fermion field in a spacetime background with an arbitrary number of toroidally compactified spatial dimensions in the presence of a non-vanishing chemical potential. Periodicity conditions along compact dimensions are taken with arbitrary phases and the presence of a constant gauge field is assumed. The latter gives rise to Aharonov-Bohm-like effects on the expectation values. They are periodic functions of magnetic fluxes enclosed by compact dimensions with t…
We prove that, in a general higher derivative theory of gravity coupled to abelian gauge fields and neutral scalar fields, the entropy and the near horizon background of a rotating extremal black hole is obtained by extremizing an entropy function which depends only on the parameters labeling the near horizon background and the electric and magnetic charges and angular momentum carried by the black hole. If the entropy function has a unique extremum then this extremum must be independent of the asymptotic values of the moduli scalar fields and the solution exhibits attractor behaviour. If the …
Vacuum expectation values (VEVs) of the current densities for charged scalar and Dirac spinor fields are investigated in (D+1)-dimensional de Sitter (dS) spacetime with toroidally compactified spatial dimensions. Along compact dimensions we impose quasiperiodicity conditions with arbitrary phases. In addition, the presence of a classical constant gauge field is assumed. The VEVs of the charge density and of the components for the current density along noncompact dimensions vanish. The gauge field leads to Aharonov-Bohm-like oscillations of the components along compact dimensions as functions o…
We evaluate the Hadamard function and the vacuum expectation value (VEV) of the current density for a charged scalar field, induced by flat boundaries in spacetimes with an arbitrary number of toroidally compactified spatial dimensions. The field operator obeys the Robin conditions on the boundaries and quasiperiodicity conditions with general phases along compact dimensions. In addition, the presence of a constant gauge field is assumed. The latter induces Aharonov-Bohm-type effect on the VEVs. There is a region in the space of the parameters in Robin boundary conditions where the vacuum stat…
We evaluate the Hadamard function and the vacuum expectation value (VEV) of the current density for a charged scalar field in the region between two co-dimension one branes on the background of locally AdS spacetime with an arbitrary number of toroidally compactified spatial dimensions. Along compact dimensions periodicity conditions are considered with general values of the phases and on the branes Robin boundary conditions are imposed for the field operator. In addition, we assume the presence of a constant gauge field. The latter gives rise to Aharonov-Bohm type effect on the vacuum current…
We investigate the fermionic condensate and the vacuum expectation value of the energy-momentum tensor for a massive fermionic field in the geometry of two parallel plate on the background of Minkowski spacetime with an arbitrary number of toroidally compactified spatial dimensions, in the presence of a constant gauge field. Bag boundary conditions are imposed on the plates and periodicity conditions with arbitrary phases are considered along the compact dimensions. The boundary induced parts in the fermionic condensate and the vacuum energy density are negative, with independence of the phase…
We investigate combined effects of topology and boundaries on the vacuum expectation value (VEV) of the fermionic current in the space with an arbitrary number of toroidally compactified dimensions. As a geometry of boundaries we consider two parallel plates on which the fermion field obeys bag boundary conditions. Along the compact dimensions, periodicity conditions are imposed with arbitrary phases. In addition, the presence of a constant gauge field is assumed. The nontrivial topology gives rise to an Aharonov-Bohm effect for the fermionic current induced by the gauge field. It is shown tha…
We derive a closed expression for the vacuum expectation value (VEV) of the fermionic current density in a (D+1)-dimensional locally AdS spacetime with an arbitrary number of toroidally compactified Poincare spatial dimensions and in the presence of a constant gauge field. The latter can be formally interpreted in terms of a magnetic flux treading the compact dimensions. In the compact subspace, the field operator obeys quasiperiodicity conditions with arbitrary phases. The VEV of the charge density is zero and the current density has nonzero components along the compact dimensions only. They …
The vacuum expectation value (VEV) of the fermionic current density is investigated in the geometry of two parallel branes in locally AdS spacetime with a part of spatial dimensions compactified to a torus. Along the toral dimensions quasiperiodicity conditions are imposed with general phases and the presence of a constant gauge field is assumed. Different types of boundary conditions are discussed on the branes, including the bag boundary condition and the conditions arising in $Z_{2}$-symmetric braneworld models. Nonzero vacuum currents appear along the compact dimensions only. In the region…
