Exact Vacuum Research Articles

Asymptotic quasinormal frequencies of brane-localized black hole

The asymptotic quasinormal frequencies of the brane-localized (4+n)-dimensional black hole are computed. Since the induced metric on the brane is not an exact vacuum solution of the Einstein equation defined on the brane, the real parts of the quasinormal frequencies ω do not approach to the well-known value THln3 but approach to THlnkn, where kn is a number dependent on the extra dimensions. For the scalar field perturbation Re(ω/TH)=ln3 is reproduced when n=0. For n≠0, however, Re(ω/TH) is smaller than ln3. It is shown also that when n>4, Im(ω/TH) vanishes in the scalar field perturbation. For the gravitational perturbation it is shown that Re(ω/TH)=ln3 is reproduced when n=0 and n=4. For different n, however, Re(ω/TH) is smaller than ln3. When n=∞, for example, Re(ω/TH) approaches to ln(1+2cos5π)≈0.906. Unlike the scalar field perturbation Im(ω/TH) does not vanish regradless of the number of extra dimensions.

Two-magnon Raman scattering in spin ladders with exact singlet-rung ground state

We suggest a family of spin-ladder models with exact singlet-rung vacuum. In addition to the terms describing interactions along legs and rungs the Hamiltonian has frustration and cyclic terms. Using coordinate Bethe ansatze all one- and two-dimensional states are constructed. The explicit formula for zero-temperature Raman scattering cross section is derived. The corresponding line-shapes are strongly asymmetric and have no more than one van-Hove singularity. The results are in good agreement with experimental data.

On the Coulomb branch of a marginal deformation of Script N = 4 SUSY Yang-Mills

We determine the exact vacuum structure of a marginal deformation of N=4 SUSY Yang-Mills with gauge group U(N). The Coulomb branch of the theory consists of several sub-branches which are governed by complex curves of the form Sigma_{n_{1}} U Sigma_{n_{2}} U Sigma_{n_{3}} of genus N=n_{1}+n_{2}+n_{3}. Each sub-branch intersects with a family of Higgs and Confining branches permuted by SL(2,Z) transformations. We determine the curve by solving a related matrix model in the planar limit according to the prescription of Dijkgraaf and Vafa, and also by explicit instanton calculations using a form of localization on the instanton moduli space. We find that Sigma_{n} coincides with the spectral curve of the n-body Ruijsenaars-Schneider system. Our results imply that the theory on each sub-branch is holomorphically equivalent to certain five-dimensional gauge theory with eight supercharges. This equivalence also implies the existence of novel confining branches in five dimensions.

Duality in Yang’s theory of gravity

The historical route and the current status of a curvature-squared model of gravity, in the affine form proposed by Yang, is briefly reviewed. Due to its inherent scale invariance, it enjoys some advantage for quantization, similarly as internal Yang-Mills fields. However, the exact vacuum solutions with double duality properties exhibit a ‘vacuum degeneracy’. By modifying the duality via a scale breaking term, we demonstrate that only the Einstein equations with induced cosmological constant emerge for the classical background, even when coupled to matter sources.

Rotating neutron stars: an invariant comparison of approximate and numerical space-time models

We compare three different models of rotating neutron star spacetimes: i) the Hartle-Thorne (1968) slow-rotation approximation, keeping terms up to second order in the stellar angular velocity; ii) the exact analytic vacuum solution of Manko et al. (2000a, 2000b); and iii) a numerical solution of the full Einstein equations. In the first part of the paper we estimate the limits of validity of the slow-rotation expansion by computing relative errors in the spacetime’s quadrupole moment Q and in the corotating and counterrotating radii of Innermost Stable Circular Orbits (ISCOs) R±. We integrate the Hartle-Thorne structure equations for five representative equations of state. Then we match these models to numerical solutions of the Einstein equations, imposing the condition that the gravitational mass and angular momentum of the models be the same. We find that the Hartle-Thorne approximation gives very good predictions for the ISCO radii, with R± accurate to better than 1% even for the fastest millisecond pulsars. At these rotational rates the accuracy on Q is � 20%, and better for longer periods. In the second part of the paper we focus on the exterior vacuum spacetimes, comparing the Hartle-Thorne approximation and the Manko analytic solution to the numerical models using Newman-Penrose (NP) coordinateindependent quantities. For all three spacetimes we introduce a physically motivated ‘quasi-Kinnersley’ NP frame. In this frame we evaluate a quantity, the speciality index S, measuring the deviation of each stellar model from Petrov Type D. Deviations from speciality on the equatorial plane are smaller than 5% at star radii for the faster rotating models, and rapidly decrease for slower rotation rates and with distance. We find that, at leading order, the deviation from Type D is proportional to (Q QKerr). Our main conclusion is that the Hartle-Thorne approximation is very reliable for most astrophysical applications.

Running Newton constant, improved gravitational actions, and galaxy rotation curves

A renormalization group (RG) improvement of the Einstein-Hilbert action is performed which promotes Newton's constant and the cosmological constant to scalar functions on spacetime. They arise from solutions of an exact RG equation by means of a ``cutoff identification'' which associates RG scales to the points of spacetime. The resulting modified Einstein equations for spherically symmetric, static spacetimes are derived and analyzed in detail. The modifications of the Newtonian limit due to the RG evolution are obtained for the general case. As an application, the viability of a scenario is investigated where strong quantum effects in the infrared cause Newton's constant to grow at large (astrophysical) distances. For two specific RG trajectories exact vacuum spacetimes modifying the Schwarzschild metric are obtained by means of a solution-generating Weyl transformation. Their possible relevance to the problem of the observed approximately flat galaxy rotation curves is discussed. It is found that a power law running of Newton's constant with a small exponent of the order ${10}^{\ensuremath{-}6}$ would account for their non-Keplerian behavior without having to postulate the presence of any dark matter in the galactic halo.

Remarks on some vacuum solutions of scalar-tensor cosmological models

We present a class of exact vacuum solutions corresponding to de Sitter and warm inflation models in the framework of scalar-tensor cosmologies. We show that in both cases the field equations reduce to planar dynamical systems with constraints. Then, we carry out a qualitative analysis of the models by examining the phase diagrams of the solutions near the equilibrium points.

Rotating black hole solution in a generalized topological 3D gravity with torsion

A first order version of topological massive gravity is achieved by liberating its translational gauge degrees of freedom. In three dimensions, our Lagrangian consists of Chern-Simons (CS) terms for curvature and torsion inducing an effective cosmological constant dynamically, whereas a ``mixed'' CS term is substituting for the topological related Einstein-Cartan action. Anti--de Sitter and rotating black hole configurations are exact vacuum solutions. They also apply to a large class of Yang-Mills-type generalizations including ``exotic'' terms exclusively permitted in 3D. The reason for this can be partially traced back to a new strong/weak duality of the translational and rotational dynamical degrees of freedom.

On correlation functions in the perturbed minimal models [formula omitted

Two-point correlation functions of spin operators in the minimal models M p,p′ perturbed by the field Φ 13 are studied in the framework of conformal perturbation theory [Nucl. Phys. B 348 (1991) 619]. The first-order corrections for the structure functions are derived analytically in terms of gamma functions. Together with the exact vacuum expectation values of local operators, this gives the short-distance expansion of the correlation functions. The long-distance behaviors of these correlation functions in the case M 2,2n+1 have been worked out using a form-factor bootstrap approach. The results of numerical calculations demonstrate that the short- and long-distance expansions match at the intermediate distances. Including the descendent operators in the OPE drastically improves the convergency region. The combination of the two methods thus describes the correlation functions at all length scales with good precision.

Critical points of glueball superpotentials and equilibria of integrable systems

We compare the matrix model and integrable system approaches to calculating the exact vacuum structure of general N=1 deformations of either the basic N=2 theory or its generalization with a massive adjoint hypermultiplet, the N=2* theory. We show that there is a one-to-one correspondence between arbitrary critical points of the Dijkgraaf-Vafa glueball superpotential and equilibrium configurations of the associated integrable system. The latter being either the periodic Toda chain, for N=2, or the elliptic Calogero-Moser system, for N=2*. We show in both cases that the glueball superpotential at the crtical point equals the associated Hamiltonian. Our discussion includes an analysis of the vacuum structure of the N=1* theory with an arbitrary tree-level superpotential for one of the adjoint chiral fields.

Letter: Some Remarks on Standing Gravitational Waves

An intuitive definition of standing gravitational waves is proposed. Some main classes of exact vacuum solutions are searched for standing gravitational waves, in most cases with a negative result. Only some Einstein–Rosen waves meet the conditions.

On the third level descendent fields in the Bullough–Dodd model and its reductions

Exact vacuum expectation values of the third level descendent fields 〈(∂ϕ)3(∂̄ϕ)3eaϕ〉 in the Bullough–Dodd model are proposed. By performing quantum group restrictions, we obtain 〈L−3L̄−3Φlk〉 in perturbed minimal conformal field theories.

An exact, asymptotically flat, vacuum solution of Einstein's equations with closed timelike curves

Solutions of Einstein's equations representing spacetimes with closed timelike curves (CTC) are commonly dismissed as unrealistic. Recently I published approximate solutions, containing CTC, which refer to ordinary sources. In this paper I present an exact vacuum solution, asymptotically flat, which contains CTC. It represents a massless rotating rod of finite length, and I give reasons why addition of mass would not abolish the CTC. I suggest that there is now an urgent need for a realistic physical interpretation of CTC in general relativity.

Liouville field theory coupled to a critical Ising model: non-perturbative analysis, duality and applications

Two different kinds of interactions between a Z n -parafermionic and a Liouville field theory are considered. For generic values of n, the effective central charges describing the UV behavior of both models are calculated in the Neveu–Schwarz sector. For n=2 exact vacuum expectation values of primary fields of the Liouville field theory, as well as the first descendent fields are proposed. For n=1, known results for sinh-Gordon and Bullough–Dodd models are recovered whereas for n=2, exact results for these two integrable coupled Ising–Liouville models are shown to exchange under a weak–strong coupling duality relation. In particular, exact relations between the parameters in the actions and the mass of the particles are obtained. At specific imaginary values of the coupling and n=2, we use previous results to obtain exact information about: (a) integrable coupled models like Ising– M p/p′ , homogeneous sine-Gordon model SU(3) 2 or the Ising–XY model, (b) Neveu–Schwarz sector of the Φ 13 integrable perturbation of N=1 supersymmetric minimal models. Several non-perturbative checks are done, which support the exact results.

Plane-symmetric analogue ofNUT space

In this paper on the basis of a new definition of spacetime symmetry,which is in accordance with the symmetry of the curvature invariants, weinvestigate exact vacuum solutions of Einstein field equationscorresponding to both static and stationary plane-symmetricspacetimes using the concepts of the (1 + 3)-decomposition orthreading formalism. Demanding thepresence of a plane-symmetricgravitomagnetic field we find a family oftwo-parameter (m and ℓ) solutions,every member of which is a plane-symmetric analogue of NUT space.

Expectation values of descendent fields in the Bullough–Dodd model and related perturbed conformal field theories

The exact vacuum expectation values of the second level descendent fields 〈(∂ϕ) 2( ∂ ̄ ϕ) 2e aϕ〉 in the Bullough–Dodd model are calculated. By performing quantum group restrictions, we obtain 〈L −2 L ̄ −2Φ lk〉 in the Φ 12, Φ 21 and Φ 15 perturbed minimal CFTs. In particular, the exact expectation value 〈T T ̄ 〉 is found to be proportional to the square of the bulk free energy.

One-point functions in integrable coupled minimal models

We propose exact vacuum expectation values of local fields for a quantum group restriction of the $C_2^{(1)}$ affine Toda theory which corresponds to two coupled minimal models. The central charge of the unperturbed models ranges from $c=1$ to $c=2$, where the perturbed models correspond to two magnetically coupled Ising models and Heisenberg spin ladders, respectively. As an application, in the massive phase we deduce the leading term of the asymptotics of the two-point correlation functions.

Proton-neutron self-consistent quasiparticle random phase approximation within the O(5) model

The self-consistent quasiparticle random phase approximation (SCQRPA) within the O(5) model in the coupled proton-neutron representation is analyzed. The exact vacuum wave function is used to compute all involved matrix elements. A stability analysis of the stationary points is performed. A phase transition from the uncoupled to the coupled stable proton-neutron regime beyond the QRPA breakdown value of the particle-particle strength is evidenced. The excitation energies are close to the lowest stable exact eigenvalues given by the diagonalization procedure for all cases. The conditions for which the Ikeda sum rule is fulfilled for all values of the particle-particle strength are pointed out.

Exotic spacetimes, superconducting strings with linear momentum, and (not quite) all that

We derive the general exact vacuum metrics associated with a stationary (non static), non rotating, cylindrically symmetric source. An analysis of the geometry described by these vacuum metrics shows that they contain a subfamily of metrics that, although admitting a consistent time orientation, display "exotic" properties, such as "trapping" of geodesics and closed causal curves through every point. The possibility that such spacetimes could be generated by a superconducting string, endowed with a neutral current and momentum, has recently been considered by Thatcher and Morgan. Our results, however, differ from those found by Thatcher and Morgan, and the discrepancy is explained. We also analyze the general possibility of constructing physical sources for the exotic metrics, and find that, under certain restrictions, they must always violate the dominant energy condition (DEC). We illustrate our results by explicitly analyzing the case of concentric shells, where we find that in all cases the external vacuum metric is non exotic if the matter in the shells satisfies the DEC.

Point and line boundaries in scalar Casimir theory

A simple image-charge construction enables one to insert point or line boundaries (or planar or hyperplanar boundaries when sufficiently many spatial dimensions are available) at or into the central point, line, plane etc., of a great range of spatial backgrounds in quantum field theory which have appropriate symmetry. This nontrivial construction (which provides among other things the exact vacuum stress tensor Tμν of the quantum field if Tμν can be computed for the original background prior to point, line,…, insertion) works if all directions xi perpendicular to the inserted object are symmetric under xi→−xi. In other respects the symmetric spatial background can be quite arbitrary. While the inserted object experiences (by symmetry) no net Casimir force from the background, it does exert Casimir forces throughout this background which were originally not present. In addition to general theory, detailed examples are given (which include exact field Tμν’s and exact Casimir force densities) for arbitrary spatial dimension. First: point and line boundaries in otherwise empty space; then a planar boundary with a semi-infinite line extending from one side; finally, parallel planar boundaries with a point boundary halfway between them. Only scalar quantum fields are analyzed here; however the extension to the electromagnetic Casimir effect is discussed qualitatively.