Curved Background Spacetime Research Articles

Generalized Gross-Neveu models and chiral symmetry breaking from string theory

We consider intersecting D-brane models which have two dimensional chiral fermions localized at the intersections. At weak coupling, the interactions of these fermions are described by generalized Gross-Neveu models. At strong coupling, these configurations are described by the dynamics of probe D-branes in a curved background spacetime. We study patterns of dynamical chiral symmetry breaking in these models at weak and strong coupling, and also discuss relationships between these two descriptions.

A Relativistic Version of the Ghirardi–Rimini–Weber Model

Carrying out a research program outlined by John S. Bell in 1987, we arrive at a relativistic version of the Ghirardi-Rimini-Weber (GRW) model of spontaneous wavefunction collapse. The GRW model was proposed as a solution of the measurement problem of quantum mechanics and involves a stochastic and nonlinear modification of the Schrödinger equation. It deviates very little from the Schrödinger equation for microscopic systems but efficiently suppresses, for macroscopic systems, superpositions of macroscopically different states. As suggested by Bell, we take the primitive ontology, or local beables, of our model to be a discrete set of space-time points, at which the collapses are centered. This set is random with distribution determined by the initial wavefunction. Our model is nonlocal and violates Bell’s inequality though it does not make use of a preferred slicing of space-time or any other sort of synchronization of spacelike separated points. Like the GRW model, it reproduces the quantum probabilities in all cases presently testable, though it entails deviations from the quantum formalism that are in principle testable. Our model works in Minkowski space-time as well as in (well-behaved) curved background space-times.

Second-order gravitational self-force

We derive an expression for the second-order gravitational self-force that acts on a self-gravitating compact object moving in a curved background spacetime. First we develop a new method of derivation and apply it to the derivation of the first-order gravitational self-force. Here we find that our result conforms with the previously derived expression. Next we generalize our method and derive a new expression for the second-order gravitational self-force. This study also has a practical motivation: The data analysis for the planned gravitational wave detector LISA requires construction of waveform templates for the expected gravitational waves. Calculation of the two leading orders of the gravitational self-force will enable one to construct highly accurate waveform templates, which are needed for the data analysis of gravitational waves that are emitted from extreme mass-ratio binaries.

Electromagnetic and gravitational self-force on a relativistic particle from quantum fields in curved space

We provide a quantum field theoretical derivation of the Abraham-Lorentz-Dirac (ALD) equation, describing the motion of an electric point charge sourcing an electromagnetic field, which back-reacts on the charge as a self-force, and the Mino-Sasaki-Tanaka-Quinn-Wald (MSTQW) equation describing the motion of a point mass with self-force interacting with the linearized metric perturbations caused by the mass off an otherwise vacuous curved background spacetime. We regularize the formally divergent self-force by smearing the direct part of the retarded Green's function and using a quasilocal expansion. We also derive the ALD-Langevin and the MSTQW-Langevin equations with a classical stochastic force accounting for the effect of the quantum fluctuations in the field, which causes small fluctuations on the particle trajectory. These equations will be useful for studying the stochastic motion of charges and small masses under the influence of both quantum and classical noise sources, derived either self-consistently or put in by hand phenomenologically. We also show that history-dependent noise-induced drift motions could arise from such stochastic sources on the trajectory that could be a hidden feature of gravitational wave forms hitherto unknown.

Energy–Momentum Pseudo-Tensor of Relic Gravitational Wave ofBoth the Polarized States

Unlike usual celestial gravitational waves, the relic gravitationalwaves (RGWs) form random signals in curved spacetime background. Wecalculate the energy–momentum pseudo-tensor of a certain component ofthe RGWs propagating along arbitrary directions in Cartesiancoordinates. It is found that the energy density of RGWs is positivedefinitely, and the momentum density components have reasonablebehaviour. Such results may provide a theoretical basis for the detection of RGWs.

Construction of the second-order gravitational perturbations produced by a compact object

Accurate calculation of the gradual inspiral motion in an extreme mass-ratio binary system, in which a compact object inspiral towards a supermassive black hole requires calculation of the interaction between the compact object and the gravitational perturbations that it induces. These metric perturbations satisfy linear partial differential equations on a curved background space-time induced by the supermassive black hole. At the point-particle limit the second-order perturbations equations have source terms that diverge as ${r}^{\ensuremath{-}4}$, where $r$ is the distance from the particle. This singular behavior renders the standard retarded solutions of these equations ill defined. Here we resolve this problem and construct well-defined and physically meaningful solutions to these equations. We recently presented an outline of this resolution [E. Rosenthal, Phys. Rev. D 72, 121503 (2005).]. Here we provide the full details of this analysis. These second-order solutions are important for practical calculations: the planned gravitational-wave detector LISA requires preparation of waveform templates for the potential gravitational waves. Construction of templates with desired accuracy for extreme mass-ratio binaries requires accurate calculation of the inspiral motion including the interaction with the second-order gravitational perturbations.

Maxwell–Chern–Simons theory for curved spacetime backgrounds

We consider a modified version of four-dimensional electrodynamics, which has a photonic Chern–Simons-like term with spacelike background vector in the action. Light propagation in curved spacetime backgrounds is discussed using the geometrical-optics approximation. The corresponding light path is modified, which allows for new effects. In a Schwarzschild background, for example, there now exist stable bounded orbits of light rays and the two polarization modes of light rays in unbounded orbits can have different gravitational redshifts.

Spacetime reduction of large N flavor models: A fundamental theory of emergent local geometry?

We introduce a novel spacetime reduction procedure for the fields of a supergravity–Yang–Mills theory in generic curved spacetime background, and with large N flavor group, to linearized forms on an infinitesimal patch of local tangent space at a point in the spacetime manifold. Our new prescription for spacetime reduction preserves all of the local symmetries of the continuum field theory Lagrangian in the resulting zero-dimensional matrix Lagrangian, thereby obviating difficulties encountered in previous matrix proposals for emergent spacetime in recovering the full nonlinear symmetries of Einstein gravity. It also obviates the challenges that must be faced by any proposal for a fundamental theory, holographic or topological, where gravity emerges instead as an induced interaction. We conjecture that the zero-dimensional matrix model obtained by this prescription for spacetime reduction of the circle-compactified type I–I′–mIIA–IIB–heterotic supergravity–Yang–Mills theory with sixteen supercharges and large N flavor group, and inclusive of the full spectrum of D p-brane charges, − 2 ⩽ p ⩽ 9 , offers a potentially complete framework for nonperturbative String/M theory. We analyze the matrix Lagrangian in detail, comparing with the results of traditional planar reduction, and clarifying the emergence of the spacetime continuum in the large N limit of the zero-dimensional matrix model. We explain the relationship of our conjecture for a fundamental theory of emergent local spacetime geometry to recent investigations of the hidden symmetry algebra of M theory, stressing insights that are to be gained from the algebraic perspective. We conclude with a list of open questions and directions for future work.

Symplectic structure for elastic and chiral conducting cosmic string models

This article is based on the covariant canonical formalism and corresponding symplectic structure on phase space developed by Witten, Zuckerman, and others in the context of field theory. After recalling the basic principles of this procedure, we construct the conserved bilinear symplectic current for generic elastic string models. These models describe current carrying cosmic strings evolving in an arbitrary curved background spacetime. Particular attention is paid to the special case of the chiral string for which the worldsheet current is null. Different formulations of the chiral string action are discussed in detail, and as a result the integrability property of the chiral string is clarified.

On a gauge invariant description of soliton dynamics

AbstractWe present important elements of a gauge and diffeomorphism invariant formulation of the moduli space approximation to soliton dynamics. We argue that explicit velocity‐dependent modifications are determined entirely from gauge and diffeomorphism invariance. We illustrate the formalism for the case of a Yang‐Mills theory on a curved spacetime background.

Towards a covariant canonical formulation for closed topological defects without boundaries

On the basis of the covariant description of the canonical formalism for quantization, we present the basic elements of the symplectic geometry for a restricted class of topological defects propagating on a curved background spacetime. We discuss the future extensions of the present results.

On the Berkovits covariant quantization of GS superstring

We study the covariant quantization of the Green–Schwarz (GS) superstrings proposed recently by Berkovits. In particular, we reformulate the Berkovits approach in a way that clarifies its relation with the GS approach and allows to derive in a straightforward way its extension to curved spacetime background. We explain the procedure working explicitly in the case of the heterotic string.

Noether Charges for self-interacting quantum field theories in curved spacetimes with a Killing-vector

We consider self-interacting, perturbative quantum field theory in a curved spacetime background with a Killing vector field. We show that the action of this spacetime symmetry on interacting field operators can be implemented by a Noether charge which arises as a surface integral over the time-component of the interacting Noether current-density associated with the Killing field. The proof of this involves the demonstration of a corresponding set of Ward identities. Our work is based on the perturbative construction by Brunetti and Fredenhagen (Commun.Math.Phys. 208 (2000) 623-661) of self-interacting quantum field theories in general globally hyperbolic spacetimes.

Erratum: Closed universe in mirage cosmology [Phys. Rev. D63, 085010 (2001)

We study the cosmological evolution of the closed universe on a spherical probe brane moving in the AdS$_m\times S^n$ background and the near-horizon background of the dilatonic D-branes. The Friedmann equations describing the evolution of the brane universe, and the effective energy density and pressure simulated on the probe brane due to its motion in the curved background spacetime are obtained and analyzed. We also comment on the relevance of the spherical probe brane to the giant graviton for the special value of the probe energy.

Closed universe in mirage cosmology

We study the cosmological evolution of the closed universe on a spherical probe brane moving in the ${\mathrm{AdS}}_{m}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{n}$ background and the near-horizon background of the dilatonic D-branes. The Friedmann equations describing the evolution of the brane universe and the effective energy density and pressure simulated on the probe brane due to its motion in the curved background spacetime are obtained and analyzed. We also comment on the relevance of the spherical probe brane to the giant graviton for the special value of the probe energy.

Constrained superconducting membranes

We present a geometrical canonical description for superconducting membranes. We consider a general action which includes a general class of superconducting extended objects (strings and domain walls). The description is inspired in the ADM framework of general relativity but, instead of the standard canonical variables a different kind of phase space is considered. The Poisson algebra of the constraints and the counting of degrees of freedom is performed. The new description is illustrated considering a superconducting domain wall on a curved background spacetime.

Exact Solutions of Covariant Wave Equations with a Multipole Source Term on Curved Spacetimes

A formalism is presented for calculating exactsolutions of covariant inhomogeneous scalar and tensorwave equations whose source terms are arbitrary ordermultipoles on a curved background spacetime. The developed formalism is based on the theory ofthe higher-order fundamental solutions for wave equationwhich are the distributions that satisfy theinhomogeneous wave equation with the corresponding order covariant derivatives of the Dirac deltafunction on the right-hand side. Like the classicalGreen's function for a scalar wave equation, thehigher-order fundamental solutions contain a direct termwhich has support on the light cone as well as a tailterm which has support inside the light cone. Knowinghow to compute the fundamental solutions of arbitraryorder, one can find exact multipole solutions of wave equations on curved spacetimes. Wepresent complete recurrent algorithms for calculatingthe arbitrary-order fundamental solutions and the exactmultipole solutions in a form convenient for practical computations. As an example we apply thealgorithm to a massless scalar wave field on aparticular Robertson-Walker spacetime.

Consistent field equations for higher spin on curved spacetimes

AbstractThe field equations proposed by Buchdahl and Wünsch for a classical spinor field with any spin quantum number on a curved spacetime background are reported. These equations do not suffer from the inconsistencies of the earlier attempts and thus solve a long‐standing problem.

Consistent field equations for higher spin on curved spacetimes

The field equations proposed by Buchdahl and Wünsch for a classical spinor field with any spin quantum number on a curved spacetime background are reported. These equations do not suffer from the inconsistencies of the earlier attempts and thus solve a long-standing problem.

DIMENSIONAL REDUCTION

Using an octonionic formalism, we introduce a new mechanism for reducing ten space–time dimensions to four without compactification. Applying this mechanism to the free, ten-dimensional, massless (momentum space) Dirac equation results in a particle spectrum consisting of exactly three generations. Each generation contains one massive spin-1/2 particle with two spin states, one massless spin-1/2 particle with only one helicity state, and their antiparticles — precisely one generation of leptons. There is also a single massless spin-1/2 particle/antiparticle pair with the opposite helicity and no generation structure. We conclude with a discussion of some further consequences of this approach, including those which could arise when using the formalism on a curved space–time background, as well as the implications for the nature of space–time itself.