Massive Vector Theory Research Articles

On the (A)dS decoupling limits of massive gravity

We consider various decoupling limits of ghost-free massive gravity on (A)dS. The first is a decoupling limit on AdS space where the mass goes to zero while the AdS radius is held fixed. This results in an interacting massive Proca vector theory with a Λ2 ∼ (MPlm)1/2 strong coupling scale which is ghost-free by construction and yet can not be put in the form of the generalized Proca theories considered so far. We comment on the existence of a potential duality between this Proca theory and a CFT on the boundary. The second decoupling limit we consider is a new limit on dS, obtained by sending the mass towards the finite partially massless value. We do this by introducing the scalar Stückelberg field which restores the partially massless symmetry. For generic values of the parameters, only a finite number of operators enter the partially massless decoupling limit and take the form of dS Galileons. If the interactions are chosen to be precisely those of the ‘candidate’ non-linear partially massless theory, the resulting strong coupling scale has a higher value and the resulting decoupling limit includes an infinite number of interactions which we give in closed form. These interactions preserve both the linear partially massless symmetry and the dS version of the Galileon shift symmetry.

Extended vector-tensor theories

Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.

Anisotropic cosmological solutions in massive vector theories

In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component v of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate Σ and the isotropic expansion rate H remains nearly constant in the radiation-dominated epoch. In the regime where Σ/H is constant, the spatial vector component v works as a dark radiation with the equation of state close to 1/3. During the matter era, the ratio Σ/H decreases with the decrease of v. As long as the conditions |Σ| ≪ H and v2 ≪ ϕ2 are satisfied around the onset of late-time cosmic acceleration, where ϕ is the temporal vector component, we find that the solutions approach the isotropic de Sitter fixed point (Σ = 0 = v) in accordance with the cosmic no-hair conjecture. In the presence of v and Σ the early evolution of the dark energy equation of state wDE in the radiation era is different from that in the isotropic case, but the approach to the isotropic value wDE(iso) typically occurs at redshifts z much larger than 1. Thus, apart from the existence of dark radiation, the anisotropic cosmological dynamics at low redshifts is similar to that in isotropic generalized Proca theories. In beyond-generalized Proca theories the only consistent solution to avoid the divergence of a determinant of the dynamical system corresponds to v = 0, so Σ always decreases in time.

Holography for Schrödinger backgrounds

We discuss holography for Schrodinger solutions of both topologically massive gravity in three dimensions and massive vector theories in (d+1) dimensions. In both cases the dual field theory can be viewed as a d-dimensional conformal field theory (two dimensional in the case of TMG) deformed by certain operators that respect the Schrodinger symmetry. These operators are irrelevant from the viewpoint of the relativistic conformal group but they are exactly marginal with respect to the non-relativistic conformal group. The spectrum of linear fluctuations around the background solutions corresponds to operators that are labeled by their scaling dimension and the lightcone momentum k_v. We set up the holographic dictionary and compute 2-point functions of these operators both holographically and in field theory using conformal perturbation theory and find agreement. The counterterms needed for holographic renormalization are non-local in the v lightcone direction.

QUANTUM AND CLASSICAL GAUGE SYMMETRIES IN A MODIFIED QUANTIZATION SCHEME

The use of the mass term as a gauge fixing term has been studied by Zwanziger, Parrinello and Jona-Lasinio, which is related to the nonlinear gauge [Formula: see text] of Dirac and Nambu in the large mass limit. We have recently shown that this modified quantization scheme is in fact identical to the conventional local Faddeev–Popov formula without taking the large mass limit, if one takes into account the variation of the gauge field along the entire gauge orbit and if the Gribov complications can be ignored. This suggests that the classical massive vector theory, for example, is interpreted in a more flexible manner either as a gauge invariant theory with a gauge fixing term added, or as a conventional massive nongauge theory. As for massive gauge particles, the Higgs mechanics, where the mass term is gauge-invariant, has a more intrinsic meaning. It is suggested that we extend the notion of quantum gauge symmetry (BRST symmetry) not only to classical gauge theory but also to a wider class of theories whose gauge symmetry is broken by some extra terms in the classical action. We comment on the implications of this extended notion of quantum gauge symmetry.

REDUCED PHASE SPACE QUANTIZATION OF MASSIVE VECTOR THEORY

We quantize massive vector theory in such a way that it has a well-defined massless limit. In contrast to the approach by Stückelberg where ghost fields are introduced to maintain manifest Lorentz covariance, we use reduced phase space quantization with nonlocal dynamical variables which in the massless limit smoothly turn into the photons, and check explicitly that the Poincaré algebra is fulfilled. In contrast to conventional covariant quantization our approach leads to a propagator which has no singularity in the massless limit and is well behaved for large momenta. For massive QED, where the vector field is coupled to a conserved fermion current, the quantum theory of the nonlocal vector fields is shown to be equivalent to that of the standard local vector fields. An inequivalent theory, however, is obtained when the reduced nonlocal massive vector field is coupled to a nonconserved classical current.

SQUEEZED GLUON CONDENSATE AND QUARK CONFINEMENT IN THE GLOBAL COLOR MODEL OF QCD

We discuss how the presence of a squeezed gluon vacuum might lead to quark confinement in the framework of the global color model of QCD. Using reduced phase space quantization of massive vector theory we construct a Lorentz-invariant and colorless squeezed gluon condensate and show that it induces a permanent, nonlocal quark interaction (delta-function in four-momentum space), which according to Munczek and Nemirovsky might lead to quark confinement. Our approach makes it possible to relate the strength of this effective confining quark interaction to the strength of the physical gluon condensate.

A CANDIDATE FOR EXACT CONTINUUM DUAL THEORY FOR SCALAR QED3

We discuss a possible exact equivalence of the Abelian Higgs model and a scalar theory of a magnetic vortex field in 2 + 1 dimensions. The vortex model has a current-current interaction and can be viewed as a strong coupling limit of a massive vector theory. The fixed point structure of the theory is discussed and mapped into fixed points of the Higgs model.

THE FREEDMAN-TOWNSEND MODEL IN TWO AND THREE DIMENSIONS

Using a mechanism similar to that employed by Freedman and Townsend in four dimensions, we discuss a variety of two- and three-dimensional gauge theories. The simplest of these models is equivalent to the nonlinear sigma model; another corresponds to a massive vector theory. In three dimensions, there exists a gauge invariance associated with the auxiliary vector ϕμa; when we quantize, this is accommodated using both the Batalin-Vilkovisky configuration space formalism and the Batalin-Fradkin-Vilkovisky configuration space formalism. Explicit one-loop calculations in the simplest two-dimensional model are carried out. The regularization used is a variant of operator regularization, allowing one to remain in two dimensions, hence circumventing problems associated with definition of the antisymmetric tensor εμν. This model is renormalizable, with renormalization mixing the scalar field ϕa and the transverse component of the vector field Vμa.

Variations on QED in three dimensions

The quantization of three-dimensional electrodynamics in 2 + 2 De Sitter space is carried out in detail. In three dimensions we find five completely different types of quantum electrodynamics. The most interesting versions have spins +1 and/or −1. When both spins are combined as modes of a single vector potential with definite parity, then the field strength vanishes; nevertheless the theory has an infinite space of propagating physical modes. This version of three-dimensional QED is equivalent to three-dimensional singleton theory. The requirements of gauge invariance prohibit local interactions, in the classical theory and within the framework of canonical quantization, and interactions are thus limited to the boundary at spatial infinity, a torus. There are also two chiral theories, in which the physical modes have spin +1 only, or −1 only; here the field strength is not identically zero, though it vanishes on the physical subspace. The chiral theories do not have smooth limits as the curvature tends to zero. All these versions of electrodynamics are smooth limits of massive vector theories, and all can be regarded as quantized counterparts of classical Chern-Simons theory. The most standard form of three-dimensional QED has physical modes with spin zero; it is in a sense a limit of a massive theory with spin zero. In two dimensions the only physical degree of freedom is an excitation with vanishing energy and momentum, a topological mode.

A SIMPLE MANNER FOR THE QUANTIZATION OF ANOMALOUS GAUGE THEORIES

The chiral Schwinger model is a massive vector theory at the quantum level. We construct the gauge invariant action using Stueckelberg formalism from this. Then the resulting action is exactly the same as the modified action obtained by path-integral formalism. We propose a simple manner for the quantization of anomalous gauge theories.