Massless Gravity Research Articles

Path integral measure, constraints and ghosts for massive gravitons with a cosmological constant

For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the conformal factor problem of Euclidean quantum (massless) gravity. When a constraint for massive gravity is incorporated and the proper treatment of the path integral measure is taken into account one finds that, for particular choices of the DeWitt metric on the space of metrics (in fact, the same choices as in the massless case), one obtains the opposite bound on the graviton mass.

Perturbative gravity in the causal approach

Quantum theory of the gravitation in the causal approach is studied up to the second order of perturbation theory in the causal approach. We emphasize the use of cohomology methods in this framework. After describing in detail the mathematical structure of the cohomology method we apply it in three different situations: (a) the determination of the most general expression of the interaction Lagrangian; (b) the proof of gauge invariance in the second order of perturbation theory for the pure gravity system—massless and massive; (c) the investigation of the arbitrariness of the second-order chronological products compatible with renormalization principles and gauge invariance (i.e. the renormalization problem in the second order of perturbation theory). In case (a) we investigate pure gravity systems and the interaction of massless gravity with matter (described by scalars and spinors) and massless Yang–Mills fields. We obtain a difference with respect to the classical field theory due to the fact that in quantum field theory one cannot enforce the divergenceless property on the vector potential and this spoils the divergenceless property of the usual energy–momentum tensor. To correct this one needs a supplementary ghost term in the interaction Lagrangian. In all three case, the computations are more simple than by the usual methods.

Massive gravity from descent equations

Both massless and massive gravity are derived from descent equations (Wess–Zumino consistency conditions). The massive theory is a continuous deformation of the massless one.

Ghosts, strong coupling, and accidental symmetries in massive gravity

We show that the strong self-interaction of the scalar polarization of a massive graviton can be understood in terms of the propagation of an extra ghostlike degree of freedom, thus relating strong coupling to the sixth degree of freedom discussed by Boulware and Deser in their Hamiltonian analysis of massive gravity. This enables one to understand the Vainshtein recovery of solutions of massless gravity as being due to the effect of the exchange of this ghost, which gets frozen at distances larger than the Vainshtein radius. Inside this region, we can trust the two-field Lagrangian perturbatively, while at larger distances one can use the higher derivative formulation. We also compare massive gravity with other models, namely, deconstructed theories of gravity, as well as the Dvali-Gabadadze-Porrati model. In the latter case, we argue that the Vainshtein recovery process is of a different nature, not involving a ghost degree of freedom.

Perturbative Quantum Gravity and its Relation to Gauge Theory.

In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on D-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input the gravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.

Cosmic strings in dilaton gravity

We examine the metric of an isolated self-gravitating Abelian-Higgs vortex in dilatonic gravity for arbitrary coupling of the vortex fields to the dilaton. We look for solutions in both massless and massive dilaton gravity. We compare our results to existing metrics for strings in Einstein and Jordan-Brans-Dicke theory. We explore the generalization of Bogomolnyi arguments for our vortices and comment on the effects on test particles.

Null spinning strings

We quantize in detail the closed string with vanishing tension, the null closed string. For Weyl ordering of quantum operators, the spectrum is continuous and there is no critical dimension. For normal ordering, however, the usual critical dimension holds and the spectrum is finite: the field content is the same as in the field theory (infinite tension) limit of usual (closed) strings. The content of bosonic null strings is massless gravity. We carry through the local supersymmetrization of this system and find similar conclusions, normal ordered null spinning strings contain in their spectrum only the massless supergravity multiplet. However, normal ordered bosonic null strings do not have a consistent quantum interpretation, whereas null spinning strings do. It points to the likely origin of some spontaneous symmetry breakdown which generates a non-zero tension, and an infinite tower of massive states. We also consider the hamiltonian formalism for quantum null (super)strings.

Two-loop modular invariance and spin-statistics

Within the context of a class of fermionic closed string theories I explicitly show some relationships between two-loop modular invariance, factorization, correct spin-statistics and the existence of a massless gravity multiplet.

Evaluation of the massive superpropagator in the f-meson-graviton mixing model

Working within the framework of the strong gravity theory using nonpolynomial Lagrangians, we have investigated themassive superpropagator for a mixedtensor field consisting of Einstein’s massless gravity field and the strong gravity field of the massive f-meson. The final compact expression for the massive superpropagator in Euclidean co-ordinate space has the form of a one-dimensional integral characterized by poles and branch cuts. A similar integral representation has been derived for the « pure » f-meson superpropagator. The reality of both integrals is guaranteed by an averaging prescription. Numerical calculations of the massive superpropagator have been carried out both in Euclideanx-space and, for the corresponding Fourier transform, in the Symanzik region of the external momenta.

Dependence of Massive Superpropagators on the Strong and Weak Gravitational Coupling Constants

Numerical computations are presented for two massive superpropagators Sf g and S in terms of their respective coupling constants [Formula: see text] and [Formula: see text]∙S corresponds to the massive spin 2+f0 meson, while Sf g represents the superpropagator for a mixed tensor field consisting of Einstein's massless gravity field gμν and the strong gravity field fμν.It is found that both the general structure of Sf g and its asymptotic behavior in the ultraviolet limit, Sf g ~ x12 as [Formula: see text], remain basically unchanged for couplings in the range [Formula: see text]. The same conclusion holds for the massive superpropagator S in the coupling interval [Formula: see text]. All computations are carried out in Euclidean coordinate space.