We study the effective actions for massive rank-2 and rank-3 antisymmetric tensor field models in curved space-time. These models are classically equivalent to massive vector field and massive scalar field with minimal coupling to gravity respectively. We prove that effective action for massive rank-2 antisymmetric tensor field is exactly equal to one for massive vector field and effective action for massive rank-3 antisymmetric tensor field is exactly equal to one for massive scalar field. Prove is based on an identity for mass-dependent zeta-functions associated with Laplacians acting on $p$-forms.
Using the BRS techniques, we prove the existence of a local and nonlinear symmetry of the gauge fixed action of the antisymmetric tensor field model in curved background.
An analysis about the antisymmetric tensor matter fields Avdeev-Chizhov theory in a curved space-time is performed. We show, in a curved spacetime, that the Avdeev-Chizhov theory can be seen as a kind of a $λϕ^{4}$ theory for a "complex self-dual" field. This relationship between Avdeev-Chizhov theory and $λϕ^{4}$ theory simplify the study of tensor matter fields in a curved space-time. The energy-momentum tensor for matter fields is computed.
A renormalizable rigid supersymmetry for the four dimensional antisymmetric tensor field model in a curved space-time background is constructed. A closed algebra between the BRS and the supersymmetry operators is only realizable if the vector parameter of the supersymmetry is a covariantly constant vector field. This also guarantees that the corresponding transformations lead to a genuine symmetry of the model. The proof of the ultraviolet finiteness to all orders of perturbation theory is performed in a pure algebraic manner by using the rigid supersymmetry.
In the recent paper Buchbinder, Kirillova and Pletnev presented formal arguments concerning quantum equivalence of free massive antisymmetric tensor fields of second and third rank to the free Proca theory and massive scalar field with minimal coupling to gravity, respectively. We confirm this result using explicit covariant calculations of non-local form factors based on the heart-kernel technique, and discuss the discontinuity of quantum contributions in the massless limit.
We apply the BRST approach, previously developed for higher spin field theories, to gauge invariant Lagrangian construction for antisymmetric massive and massless bosonic fields in arbitrary d-dimensional curved space. The obtained theories are reducible gauge models both in massless and massive cases and the order of reducibility grows with the value of the rank of the antisymmetric field. In both the cases the Lagrangians contain the sets of auxiliary fields and possess more rich gauge symmetry in comparison with standard Lagrangian formulation for the antisymmetric fields. This serves addit…
We show the existence of a renormalizable local supersymmetry for the gauge fixed action of the four dimensional antisymmetric tensor field model in a curved background quantized in a generalized axial gauge. By using the technique of the algebraic renormalization procedure, we prove the ultraviolet finiteness of the model to all orders of perturbation theory.
We present an explicit proof that a minimal model of rank-2 antisymmetric field with spontaneous Lorentz violation and a classically equivalent vector field model are also quantum equivalent, by calculating quantum effective actions of both theories. We comment on the issues encountered while checking quantum equivalence in curved spacetime.
We study the quantization of a simple model of antisymmetric tensor field with spontaneous Lorentz violation in curved spacetime. We evaluate the 1-loop corrections at first order of metric perturbation, using a general covariant effective action approach. We revisit the issue of quantum equivalence, and find that it holds for non-Lorentz-violating modes but breaks down for Lorentz violating modes.
A new approach is provided to determine the dilaton--antisymmetric tensor coupling in a supergravity theory by considering the static supersymmetric field configuration around a super extended object, which is consistently formulated in a curved superspace. By this, the corresponding SUSY transformation rules can also be determined for vanishing fermionic fields as well as bosonic fields other than those in the determined coupling. Therefore, we can, in turn, use this determined part of the supergravity theory to study all the related vacuum-like solutions. We have determined the dilaton--anti…
We describe how to construct and compute unambiguously path integrals for particles moving in a curved space, and how these path integrals can be used to calculate Feynman graphs and effective actions for various quantum field theories with external gravity in the framework of the worldline formalism. In particular, we review a recent application of this worldline approach and discuss vector and antisymmetric tensor fields coupled to gravity. This requires the construction of a path integral for the N=2 spinning particle, which is used to compute the first three Seeley-DeWitt coefficients for …
We show that the field equations for the supercoordinates and the self--dual antisymmetric tensor field derived from the recently constructed kappa-invariant action for the M theory five-brane are equivalent to the equations of motion obtained in the doubly supersymmetric geometrical approach at the worldvolume component level.
We consider a complex Hermitian manifold of complex dimensions four with a Hermitian metric and a Chern connection. It is shown that the action that determines the dynamics of the metric is unique, provided that the linearized Einstein action coupled to an antisymmetric tensor is obtained, in the limit when the imaginary coordinates vanish. The unique action is of the Chern-Simons type when expressed in terms of the Kähler form. The antisymmetric tensor field has gauge transformations coming from diffeomorphism invariance in the complex directions. The equations of motion must be supplemented …
One can describe an $n$-dimensional noncommutative torus by means of an antisymmetric $n\times n$-matrix $θ$. We construct an action of the group $SO(n,n|\bf Z)$ on the space of antisymmetric matrices and show that, generically, matrices belonging to the same orbit of this group give Morita equivalent tori. Some applications to physics are sketched.
The origin of matter-antimatter asymmetry is one of the most important outstanding problems at the interface of particle physics and cosmology. Gravitational leptogenesis (baryogenesis) provides a possible mechanism through explicit couplings of spacetime curvature to appropriate lepton (or baryon) currents. In this paper, the idea that these strong equivalence principle violating interactions could be generated automatically through quantum loop effects in curved spacetime is explored, focusing on the realisation of the discrete symmetries C, CP and CPT which must be broken to induce matter-a…
We show that the recently formulated Equivalence Principle (EP) implies a basic cocycle condition both in Euclidean and Minkowski spaces, which holds in any dimension. This condition, that in one-dimension is sufficient to fix the Schwarzian equation [6], implies a fundamental higher dimensional Moebius invariance which in turn univocally fixes the quantum version of the Hamilton-Jacobi equation. This holds also in the relativistic case, so that we obtain both the time-dependent Schroedinger equation and the Klein-Gordon equation in any dimension. We then show that the EP implies that masses a…
We present a self-tuning solution of the cosmological constant problem with one extra dimension which is curved with a warp factor. To separate out the extra dimension and to have a self-tuning solution, a three index antisymmetric tensor field is introduced with the $1/H^2$ term in the Lagrangian. The standard model fields are located at the $y=0$ brane. The existence \cite{kklcc} of the self-tuning solution (which results without any fine tuning among parameters in the Lagrangian) is crucial to obtain a vanishing cosmological constant in a 4D effective theory. The de Sitter and anti de Sitte…
We study quenched SU(N) gauge theories with fermions in the two-index symmetric, antisymmetric and the adjoint representations. Our main motivation is to check whether at large number of colours those theories become non-perturbatively equivalent. We prove the equivalence assuming that the charge-conjugation symmetry is not broken in pure Yang-Mills theory. We then carry out a quenched lattice simulation of the quark condensate in the symmetric, antisymmetric and the adjoint representations for SU(2), SU(3), SU(4), SU(6) and SU(8). We show that the data support the equivalence and discuss the …
In this paper a non-relativistic particle moving on a hypersurface in a curved space and the multidimensional rotator are investigated using the Hamilton-Jacobi formalism. The equivalence with the Dirac Hamiltonian formalism is demonstrated in both Cartesian and curvilinear coordinates. The energy spectrum of the multidimensional rotator is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere.
A real anti-symmetric tensor field was introduced to realize a holographic magnetic ordered phase in our previous works. However, a more careful analysis shows there is a vector ghost in the model. In this paper we present a modified Lagrangian density for the anti-symmetric tensor, which is ghost free and causality is well-defined, and keeps all the significant results in the original model qualitatively. We show this modified Lagrangian density could come from the dimensional compactification of $p$-form field in String/M-theory. For static curved space-time, we also prove that this modified…
We have calculated the hydrogen atom spectrum on curved noncommutative space defined by the commutation relations $\left[ \hat {x}^{i},\hat{x}^{j}\right] =iθ\hatω^{ij}\left( \hat {x}\right) $, where $θ$ is the parameter of noncommutativity. The external antisymmetric field which determines the noncommutativity is chosen as $ω^{ij}(x) =\varepsilon^{ijk}{x}_{k}f\left( {x_i}x^{i}\right) $. In this case the rotational symmetry of the system is conserved, preserving the degeneracy of the energy spectrum. The contribution of the noncommutativity appears as a correction to the fine structure. The cor…
We initiate a program to study the relationship between the target space, the spectrum and the scattering amplitudes in string theory. We consider scattering amplitudes following from string theory and quantum field theory on a curved target space, which is taken to be the $SU(2)$ group manifold, with special attention given to the duality between contributions from different channels. We give a simple example of the equivalence between amplitudes coming from string theory and quantum field theory, and compute the general form of a four-scalar field theoretical amplitude. The corresponding str…
Unimodular gravity (UG) is an interesting theory that may explain why the cosmological constant is extremely small, in contrast to general relativity (GR). The theory has only the transverse diffeomorphism invariance and this causes lots of debate as to the equivalence of UG to GR in the covariant quantization. We study the covariant BRST quantization of UG by gauge fixing only the transverse diffeomorphism and show that the remaining physical degrees of freedom are two, the same number as GR. This is achieved by using antisymmetric tensor ghost fields which automatically satisfy the transvers…
A gauge invariant formulation for the massive axion is considered. The axion acquires mass through a topological term which couples a (pseudo)scalar and a third rank antisymmetric tensor. Duality, local and canonical equivalences with the non-gauge invariant proposal are established. The supersymmetric version of the gauge invariant model is constructed.
Nucleation rates for tunneling processes in Minkowski and de Sitter space are investigated, taking into account one loop prefactors. In particular, we con- sider the creation of membranes by an antisymmetric tensor field, analogous to Schwinger pair production. This can be viewed as a model for the decay of false (or true) vacuum at zero temperature, in the thin wall limit. Also considered is the spontaneous nucleation of strings, domain walls and monopoles during inflation. The instantons for these processes are spherical world-sheets or world-lines embedded in flat or de Sitter backgrounds. …
We consider a new 3-parameter class of exact 4-dimensional solutions in closed string theory and solve the corresponding string model, determining the physical spectrum and the partition function. The background fields (4-metric, antisymmetric tensor, two Kaluza-Klein vector fields, dilaton and modulus) generically describe axially symmetric stationary rotating (electro)magnetic flux-tube type universes. Backgrounds of this class include both the dilatonic (a=1) and Kaluza-Klein (a=\sqrt 3) Melvin solutions and the uniform magnetic field solution, as well as some singular space-times. Solvabil…
We discuss the quantum and classical dynamics of a particle with spin in the gravitational field of a rotating source. A relativistic equation describing the motion of classical spin in curved spacetimes is obtained. We demonstrate that the precession of the classical spin is in a perfect agreement with the motion of the quantum spin derived from the Foldy-Wouthuysen approach for the Dirac particle in a curved spacetime. We show that the precession effect depends crucially on the choice of a tetrad. The results obtained are compared to the earlier computations for different tetrad gauges.
Gravity curves spacetime. In regions where the de Broglie wavelength is very small compared to the curvature of spacetime, the wave equations in flat spacetime can be generalized to curved spacetime. The validity of the formulation when the de Broglie wavelength becomes comparable to the curvature is an open question. To test these formulations experimentally, huge energy of the order of the Planck mass would be required. Euclideanized spacetime is used to model thermal systems. In this work, an equivalence between spatial variation of temperature in thermal baths and curvature of Euclideanize…
Braneworld effective action is constructed by two different methods based respectively on the Dirichlet and Neumann boundary value problems. The equivalence of these methods is shown due to nontrivial duality relations between special boundary operators of these two problems. Previously known braneworld action algorithms in two-brane Randall-Sundrum model are generalized to curved branes with deSitter and Anti-deSitter geometries.
We review a few rigorous and partly unpublished results on the regularisation of the stress-energy in quantum field theory on curved spacetimes: 1) the symmetry of the Hadamard/Seeley-DeWitt coefficients in smooth Riemannian and Lorentzian spacetimes 2) the equivalence of the local $ζ$-function and the Hadamard-point-splitting procedure in smooth static spacetimes 3) the equivalence of the DeWitt-Schwinger- and the Hadamard-point-splitting procedure in smooth Riemannian and Lorentzian spacetimes.
A massive gauge invariant formulation for scalar ($ϕ$) and antisymmetric ($C_{mnp}$) fields with a topological coupling, which provides a mass for the axion field, is considered. The dual and local equivalence with the non-gauge invariant proposal is established, but on manifolds with non-trivial topological structure both formulations are not globally equivalent.
We discuss the quantum equivalence, to all orders of perturbation theory, between the Yang-Mills theory and its first order formulation through a second rank antisymmetric tensor field. Moreover, the introduction of an additional nonphysical vector field allows us to interpret the Yang-Mills theory as a kind of perturbation of the topological BF model.
There exists a simple rule by which path integrals for the motion of a point particle in a flat space can be transformed correctly into those in curved space. This rule arose from well-established methods in the theory of plastic deformations, where crystals with defects are described mathematically by applying nonholonomic coordinate transformations to ideal crystals. In the context of time-sliced path integrals, this has given rise to a {\em quantum equivalence principle\/} which determines the measure of fluctating orbits in spaces with curvature and torsion. The nonholonomic transformation…
We show that the abelian topological mass mechanism in four dimensions, described by the Cremmer-Sherk action, can be obtained from dimensional reduction in five dimensions. Starting from a gauge invariant action in five dimensions, where the dual equivalence between a massless vector field and a massless second-rank antisymmetric field in five dimensions is established, the dimensional reduction is performed keeping only one massive mode. Furthermore, the Kalb-Ramond action and the Stuckelberger formulation for massive spin-1 are recovered.
The representation of measurements by positive operator valued measures and the description of the most general state transformations by means of completely positive maps are two basic concepts of quantum information theory. These concepts can be trivially extended to field theories in curved spacetime if all the representations of canonical commutation or anticommutation relations are unitarily equivalent. We show that both concepts can be applied even when there is no such unitary equivalence.
In this work, we revisit the duality between a self-dual non-gauge invariant theory and a topological massive theory in $3+1$ dimensions. The self-dual Lagrangian is composed by a vector field and an antisymmetric field tensor whereas the topological massive Lagrangian is build using a $B \wedge F$ term. Though the Lagrangians are quite different, they yield to equations of motion that are connected by a simple dual mapping among the fields. We discuss this duality by analyzing the degrees of freedom in both theories and comparing their propagating modes at the classical level. Moreover, we em…
We describe a global approach to the study of duality transformations between antisymmetric fields with transitions and argue that the natural geometrical setting for the approach is that of gerbes, these objects are mathematical constructions generalizing U(1) bundles and are similarly classified by quantized charges. We address the duality maps in terms of the potentials rather than on their field strengths and show the quantum equivalence between dual theories which in turn allows a rigorous proof of a generalized Dirac quantization condition on the couplings. Our approach needs the introdu…
The basic properties of Poincare gauge invariant Hilbert bundles over Lorentzian manifolds are derived. Quantum connections are introduced in such bundles, which govern a parallel transport that is shown to satisfy the strong equivalence principle in the quantum regime. Path-integral expressions are presented for boson propagators in Hilbert bundles over globally hyperbolic curved spacetimes. Their Poincare gauge covariance is proven, and their special relativistic limit is examined. A method for explicitly computing such propagators is presented for the case of cosmological models with Robert…
We investigate further the recent proposal for the form of the Matrix theory action in weak background fields. We perform DVV reduction to the multiple D0-brane action in order to find the Matrix string theory action for multiple fundamental strings in curved but weak NS-NS and R-R backgrounds. This matrix sigma model gives a definite prescription on how to deal with R-R fields with an explicit spacetime dependence in Type II string theory. We do this both via the 9-11 flip and the chain of T and S dualities, and further check on their equivalence explicitly. In order to do so, we also discuss…
The $T \bar T$ deformation of a 2 dimensional field theory living on a curved spacetime is equivalent to coupling the undeformed field theory to 2 dimensional `ghost-free' massive gravity. We derive the equivalence classically, and using a path integral formulation of the random geometries proposal, which mirrors the holographic bulk cutoff picture. We emphasize the role of the massive gravity \stu fields which describe the diffeomorphism between the two metrics. For a general field theory, the dynamics of the \stu fields is non-trivial, however for a CFT it trivializes and becomes equivalent …
A fundamentally different approach to path integral quantum mechanics in curved space-time is presented, as compared to the standard approaches currently available in the literature. Within the context of scalar particle propagation in a locally curved background, such as described by Fermi or Riemann normal co-ordinates, this approach requires use of a constructed operator to rotate the initial, intermediate, and final position ket vectors onto their respective local tangent spaces, defined at each local time step along some arbitrary classical reference worldline. Local time translation is d…
This thesis uses Path Integrals and Green's Functions to study Gravity, Quantum Field Theory and Statistical Mechanics, particularly with respect to: finite temperature quantum systems of different spin in gravitational fields; finite temperature interacting quantum systems in perturbative regime; self-interacting fermi models in non-trivial space-time of different dimensions; non-linear quantum models at finite temperatures in a background curved space-time; 3-D topological field models in non-trivial space-time and at finite temperatures; thermal quantum systems in a background curved space-…
We present a unified description of temperature and entropy in spaces with either "true" or "accelerated observer" horizons: In their (higher dimensional) global embedding Minkowski geometries, the relevant detectors have constant accelerations a_{G}; associated with their Rindler horizons are temperature a_{G}/2πand entropy equal to 1/4 the horizon area. Both quantities agree with those calculated in the original curved spaces. As one example of this equivalence, we obtain the temperature and entropy of Schwarzschild geometry from its flat D=6 embedding.
By dimensional reduction of a massive supersymmetric B$\wedge $F theory, a manifestly N=1 supersymmetric completion of a massive antisymmetric tensor gauge theory is constructed in (2+1) dimensions. In the N=1-D=3 superspace, a new topological term is used to give mass for the Kalb-Ramond field. We have introduced a massive gauge invariant model using the Stuckelberg formalism and an abelian topologically massive theory for the Kalb-Ramond superfield. An equivalence of both massive models is suggested. Further, a component field analysis is performed, showing a second supersymmetry in the mode…
In a geometrical approach to gravity the metric and the (gravitational) connection can be independent and one deals with metric-affine theories. We construct the most general action of metric-affine effective field theories, including a generic matter sector, where the connection does not carry additional dynamical fields. Among other things, this helps in identifying the complement set of effective field theories where there are other dynamical fields, which can have an interesting phenomenology. Within the latter set, we study in detail a vast class where the Holst invariant (the contraction…
It is known that the Maxwell theory in $D$ dimensions can be written in a first order form (in derivatives) by introducing a totally antisymmetric field which leads to a $(D-3)$-form dual theory. Remarkably, one can replace the antisymmetric field by a symmetric rank two tensor ($W_{μν}=W_{νμ}$). Such master action establishes the duality between the Maxwell-theory and a fourth order higher rank model in a $D$-dimensional flat space time. A naive generalization to the curved space shows a connection between the recently found D=4 critical gravity and the Maxwell theory plus a coupling term to …
The conformal anomaly in curved spacetime with antisymmetric torsion is reconsidered, taking into account new important details. We formulate, for the first time, the covariant solution of the anomaly-induced effective action. The covariant effective action includes local terms corresponding to total derivatives in the conformal anomaly. The contribution of massless fermions to these terms is characterized by multiplicative anomaly, coming from two different choices of doubling for the spinor operator. On the other hand, the nonlocal part of anomaly-induced action is free of ambiguities and ad…
Using two different methods inspired by duality transformations we present the equivalence between effective Lagrangians for massive vector mesons using a vector field and an antisymmetric tensor field. This completes the list of explicit field transformations between the various effective Lagrangian methods to describe massive vector and axial vector mesons.
We explore the quantization of a $(1+1)$-dimensional inhomogeneous scalar field theory in which Poincaré symmetry is explicitly broken. We show the `classical equivalence' between a scalar field theory on curved spacetime background and its corresponding inhomogeneous scalar field theory. This implies that a hidden connection may exist among some inhomogeneous field theories, which corresponds to general covariance in field theory on curved spacetime. Based on the classical equivalence, we propose how to quantize a specific field theory with broken Poincaré symmetry inspired by standard field …
In the Dirac-Weyl equation that describes massless neutrino propagation in the minimal Standard Model, the ($2\times 2$ equivalence of the) gamma matrices convert Weyl spinors into spacetime tensors, and vice versa. They can thus be regarded as amalgamations of three different types of mappings, one that connects particle spinors directly forming representations to internal gauge symmetries to their spacetime counterparts that are embodied by null flags, another that translates the spacetime spinors into their corresponding tensors expressed in an orthonormal tetrad, and finally a purely tenso…
Quantum phenomena such as vacuum polarisation in curved spacetime induce interactions between photons and gravity with quite striking consequences, including the violation of the strong equivalence principle and the apparent prediction of `superluminal' photon propagation. These quantum interactions can be encoded in an effective action. In this paper, we extend previous results on the effective action for QED in curved spacetime due to Barvinsky, Vilkovisky and others and present a new, local effective action valid to all orders in a derivative expansion, as required for a full analysis of th…
An extension of the notion of classical equivalence of equivalence in the Batalin--(Fradkin)--Vilkovisky (BV) and (BFV) framework for local Lagrangian field theory on manifolds possibly with boundary is discussed. Equivalence is phrased in both a strict and a lax sense, distinguished by the compatibility between the BV data for a field theory and its boundary BFV data, necessary for quantisation. In this context, the first- and second-order formulations of non-Abelian Yang--Mills and of classical mechanics on curved backgrounds, all of which admit a strict BV-BFV description, are shown to be p…
Photons propagating in curved spacetime may, depending on their direction and polarisation, have velocities exceeding the ``speed of light'' c. This phenomenon arises through vacuum polarisation in QED and is a tidal gravitational effect depending on the local curvature. It implies that the Principle of Equivalence does not hold for interacting quantum field theories in curved spacetime and reflects a quantum violation of local Lorentz invariance. These results are illustrated for the propagation of photons in the Reissner-Nordström spacetime characterising a charged black hole. A general anal…
A theory in which 4-dimensional spacetime is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza-Klein theory. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gau…
