We study the massive gravity theory proposed by Arkani-Hamed, Georgi and Schwartz. In this theory, the graviton becomes massive when general covariance is spontaneously broken through the introduction of a field that links two metrics, one of the which will eventually decouple. The excitation of this "link" field acts like a Goldstone boson in giving mass to the graviton. We work out the graviton and Goldstone boson propagators explicitly by means of gauge fixing terms similar to the renormalizability gauges used in gauge theories. With these propagators, we calculate the lowest order tree-level interaction between two external energy momentum tensors. The result is independent of the gauge parameter, but different from the prediction of massless gravity theory, i.e., general relativity. This difference remains even if the mass of the graviton goes to zero, in which case it gives the van Dam-Veltman-Zakharov (vDVZ) discontinuity between the propagators of a massive and massless linearized graviton. Moreover, we show that the Fierz-Pauli graviton mass term can be considered as the ``unitary gauge'' of a more general theory with an extra scalar field. We explicitly construct such a theory in which the vDVZ discontinuity arises with a graviton mass term that is different from the Fierz-Pauli mass term. This theory has a local Weyl symmetry under conformal transformations of the metric. In the case when the mass goes to zero, the Weyl summetry becomes a global symmetry. It is possible that the local Weyl symmetry will give a hint as to the form of the corresponding fully nonlinear theory having a nonzero graviton mass.
We investigate the graviton propagator in the type IIB supergravity background which is dual to 4 dimensional noncommutative gauge theory. We assume that the boundary is located not at the infinity but at the noncommutative scale where the string frame metric exhibits the maximum. We argue that the Neumann boundary condition is the appropriate boundary condition to be adopted at the boundary. We find that the graviton propagator behaves just as that of the 4 dimensional massless graviton. On the other hand, the non-analytic behaviors of the other Kaluza-Klein modes are not significantly affect…
The Graviton Propagator in Asymptotically Safe Gravity with Non-Local Form Factors
INAF Osservatorio Astrofisico di Catania（意大利国家天体物理研究所卡塔尼亚天文台）；INFN, Sezione di Catania（意大利国家核物理研究所卡塔尼亚分部）；Università di Catania, Dipartimento di Fisica e Astronomia（卡塔尼亚大学物理与天文学系）
A Mellin-type representation of the graviton bulk-to-bulk propagator from Ref. 1 in terms of the integral over the product of bulk-to-boundary propagators is derived.
A novel general expression is obtained for the graviton propagator from Lagrangian field theory by taking into account the necessary fact that in the functional differential approach of quantum field theory, in order to generate non-linearities in gravitation and interactions with matter, the external source $T_{μν}$, coupled to the gravitational field, should \textit{a priori} not be conserved $\partial^μT_{μν}\neq 0$, so variations with respect to its ten components may be varied \textit{independently}. The resulting propagator is the one which arises in the functional approach and does \tex…
We describe closed string modes by open Wilson lines in noncommutative (NC) gauge theories on compact fuzzy G/H in IIB matrix model. In this construction the world sheet cut-off is related to the spacetime cut-off since the string bit of the symmetric traced Wilson line carries the minimum momentum on G/H. We show that the two point correlation functions of graviton type Wilson lines in 4 dimensional NC gauge theories behave as 1/(momentum)^2. This result suggests that graviton is localized on D3-brane, so we can naturally interpret D3-branes as our universe. Our result is not limited to D3-br…
We review (and elaborate on) the `dual graviton problem' in the context of duality covariant formulations of M-theory (exceptional field theories). These theories require fields that are interpreted as components of the dual graviton in order to build complete multiplets under the exceptional groups E$_{d(d)}$, $d=2,\ldots, 9$. Circumventing no-go arguments, consistent theories for such fields have been constructed by incorporating additional covariant compensator fields. The latter fields are needed for gauge invariance but also for on-shell equivalence with $D=11$ and type IIB supergravity. …
We formulate the graviton propagator on de Sitter background in a 2-parameter family of simple gauges which break de Sitter invariance. Explicit results are derived for the first order perturbations in each parameter. These results should be useful in computations to check for gauge dependence of graviton loop corrections.
We consider the covariant graviton propagator in de Sitter spacetime in a gauge with two parameters, alpha and beta, in the Euclidean approach. We give an explicit form of the propagator with a particular choice of beta but with arbitrary value of alpha. We confirm that two-point functions of local gauge-invariant quantities do not increase as the separation of the two points becomes large.
We compute some components of the graviton propagator in loop quantum gravity, using the spinfoam formalism, up to some second order terms in the expansion parameter.
We consider the proposal of gr-qc/0508124 for the extraction of the graviton propagator from the spinfoam formalism. We propose a new ansatz for the boundary state, using which we can write the propagator as an integral over SU(2). The perturbative expansion in the Planck length can be recast into the saddle point expansion of this integral. We compute the leading order and recover the behavior expected from low-energy physics. In particular, we prove that the degenerate spinfoam configurations are suppressed.
We study the analytic structure of the resummed graviton propagator, inspired by the possible existence of black hole precursors in its spectrum. We find an infinite number of poles with positive mass, but both positive and negative effective width, and studied their asymptotic behaviour in the infinite sheet Riemann surface. We find that the stability of these precursors depend crucially on the value of the normalisation point scale.
We construct the gauge field and graviton propagators in Euclidean AdS(d+1) space-time by two different methods. In the first method the gauge invariant Maxwell or linearized Ricci operator is applied directly to bitensor ansatze for the propagators which reflect their gauge structure. This leads to a rapid determination of the physical part of the propagators in terms of elementary functions. The second method is a more traditional approach using covariant gauge fixing which leads to a solution for both physical and gauge parts of the propagators. The gauge invariant parts agree in both metho…
We construct the graviton propagator on de Sitter background in exact de Donder gauge. We prove that it must break de Sitter invariance, just like the propagator of the massless, minimally coupled scalar. Our explicit solutions for its two scalar structure functions preserve spatial homogeneity and isotropy so that the propagator can be used within the larger context of inflationary cosmology, however, it is simple to alter the residual symmetry. Because our gauge condition is de Sitter invariant (although no solution for the propagator can be) renormalization should be simpler using this prop…
We give an explicit superspace propagator for the chiral scalar field strength of 10D IIB supergravity on an AdS5 x S5 background. Because this space is conformally flat, the propagator is very simple, almost identical to that of flat space. We also give an explicit expansion over the Kaluza-Klein modes of S5. The fact that the full propagator is so much simpler suggests that, as in 2D conformal field theory, AdS/CFT calculations would be simpler without a mode expansion.
We study the graviton propagator in euclidean loop quantum gravity, using the spinfoam formalism. We use boundary-amplitude and group-field-theory techniques, and compute one component of the propagator to first order, under a number of approximations, obtaining the correct spacetime dependence. In the large distance limit, the only term of the vertex amplitude that contributes is the exponential of the Regge action: the other terms, that have raised doubts on the physical viability of the model, are suppressed by the phase of the vacuum state, which is determined by the extrinsic geometry of …
A new way to write the massive scalar and fermion propagators on a background of a weak gauge field is presented. They are written in a form that is manifestly gauge-covariant up to several additional terms that can be written as boundary terms in momentum space. These additional terms violate Ward-Takahashi identities and need to be renormalized by appropriate counterterms if the complete theory is to be gauge-covariant. This form makes it possible to calculate many amplitudes in a manifestly gauge-covariant way (at the same time reducing the number of Feynman diagrams). It also allows to exp…
We explicitly work out the de Sitter breaking contributions to the recent solution for the de Donder gauge graviton propagator on de Sitter. We also provide explicit power series expansions for the two structure functions, which are suitable for implementing dimensional regularization. And we evaluate the coincidence limit of the propagator.
We derive the graviton propagator on the brane for theories with quasi-localized gravity. In these models the ordinary 4D graviton is replaced by a resonance in the spectrum of massive Kaluza-Klein modes, which can decay into the extra dimension. We find that the effects of the extra polarization in the massive graviton propagator is exactly cancelled by the bending of the brane due to the matter sources, up to small corrections proportional to the width of the resonance. Thus at intermediate scales the classic predictions of Einstein's gravity are reproduced in these models to arbitrary preci…
We study the classical limit of the ELPR/FK spin foam models by analyzing the large-distance asymptotics of the corresponding graviton propagators. This is done by examining the large-spin asymptotics of the Hartle-Hawking wavefunction which is peaked around a classical flat spatial geometry. By using the stationary phase method we determine the wavefunction asymptotics. The obtained asymptotics does not give the desired large-distance asymptotics for the corresponding graviton propagator. However, we show that the ELPR/FK vertex amplitude can be redefined such that the corresponding Hartle-Ha…
We discuss the equivalence of the standard covariant expressions and light-front expressions of the three fundamental one loop Feynman diagrams of Quantum Electrodynamics viz. vertex correction, fermion self-energy and vacuum polarization in the light-front gauge obtained using time-ordered Hamiltonian perturbation theory. Although this issue has been addressed by us and others previously, our emphasis in this article is to resolve any ambiguity regarding the correct form of the gauge boson propagator to be used in the light-front gauge. We show how integrating over the light-front energy cons…
We construct a de Sitter invariant photon propagator in general covariant gauges. Our result is a natural generalization of the Allen-Jacobson photon propagator in Feynman gauge. Our propagator reproduces the correct response to a point static charge and the one-loop electromagnetic stress-energy tensor, strongly suggesting that it is suitable for perturbative calculations on de Sitter.
Graviton propagator diverges in certain gauges in de Sitter spacetime. We address this problem in this work by generalizing the infinitesimal BRST transformations in de Sitter spacetime to finite field-dependent BRST (FFBRST) transformations. These FFBRST transformations are symmetry of the classical action, but do not leave path integral measure invariant for the graviton theory in de Sitter spacetime. Due to the non-trivial Jacobian of such finite transformation the path integral measure changes and hence FFBRST transformation is capable of relating theories in two different gauges. We expli…
It is known that the covariant graviton two-point function in de Sitter spacetime is infrared divergent for some choices of gauge parameters. On the other hand it is also known that there are no infrared divergences requiring an infrared cutoff for the physical graviton two-point function for this spacetime in the transverse-traceless-synchronous gauge in the global coordinate system. We show in this paper that the covariant graviton Wightman two-point function with two gauge parameters is equivalent to the physical one in the global coordinate system in the sense that they produce the same tw…
We examine the scalar sector of the covariant graviton two-point function in de Sitter spacetime. This sector consists of the pure-trace part and another part described by a scalar field. We show that it does not contribute to two-point functions of gauge-invariant quantities. We also demonstrate that the long-distance growth present in some gauges is absent in this sector for a wide range of gauge parameters.
Using on-shell amplitude methods, we explore 4-dimensional Electric-Magnetic duality and its double copy. We show explicitly that the on-shell scattering amplitudes know about `dual' photons (and dual gravitons), that the off-shell photon propagator double copies to the graviton propagator and that the magnetic part of the propagator is essential for the double copy to hold. We also show that there is an equivalent gravito-magnetic part of the graviton propagator which is essential in giving rise to solutions with either angular momentum or NUT charge. Furthermore, we comment on the so-called …
We explore a connection between generalized uncertainty principle (GUP) and modified Hořava-Lifshitz (HL) gravity. The GUP density function may be replaced by the cutoff function for the renormalization group of modified Hořava-Lifshitz gravity. We find the GUP-corrected graviton propagators and compare these with tensor propagators in the HL gravity. Two are qualitatively similar, but the $p^5$-term arisen from Cotton tensor is missed in the GUP-corrected graviton propagator.
We consider the interaction between a charged scalar boson and the Bopp-Podolsky gauge fields. The Bopp-Podolsky (BP) electrodynamics possesses both massive and massless propagation modes for the photon, while preserving gauge invariance. We obtain the propagator of all fields present in the model for the higher-order generalizations of the linear covariant, light-front and doubly transverse light-front gauges. Although BP's original model is described by a higher-order derivatives Lagrangian, it is possible to work with an equivalent reduced-order version by means of the introduction of an au…
Traditional derivations of general relativity from the graviton degrees of freedom assume space-time Lorentz covariance as an axiom. In this essay, we survey recent evidence that general relativity is the unique spatially-covariant effective field theory of the transverse, traceless graviton degrees of freedom. The Lorentz covariance of general relativity, having not been assumed in our analysis, is thus plausibly interpreted as an accidental or emergent symmetry of the gravitational sector. From this point of view, Lorentz covariance is a necessary feature of low-energy graviton dynamics, not…
In this work, we investigate the consequences of the spontaneous breaking of Lorentz symmetry, triggered by the bumblebee vector field, on the usual Einstein-Hilbert theory. Specifically, we consider the Einstein-Hilbert action modified by the bumblebee dynamic field, and evaluate the graviton propagator using an extended basis of Barnes-Rivers tensor projectors, involving the Lorentz-violating vector. Once the propagator is carried out, we proceed with discussing the consistency of the model, writing the dispersion relations, and analyzing causality and unitarity. We verify that this model po…
We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions. Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been …
We examine the Dyson-Schwinger equation for the fermion propagator in quenched QED in three and four dimension based on spectral representation with vertex ansatz which preserves Ward-Takahashi Identity.An appropriate renormalization within dispersion integral smoothes the threshold behaviour of the fermion self energy in three dimension.Thus we avoid the infrared singurality in three dimension.The behaviour of the fermion propagator in three dimension near the threshold is then found to be similar to the four dimensional one.There exisit analytic solutions for arbitrary gauges and the full pr…
Some one-loop diagrams with one and two external baryons/nucleons are revisited using covariant baryon propagators in chiral effective theory. We showed that it is enough to separate and subtract all the local terms that violate chiral power counting to recover chiral power counting, no need to introduce extra operations. The structures of leading chiral corrections and IR enhancement or threshold effects are 'stable' or persist as long as covariant propagators are employed for all particles.
We give a general procedure for extracting the propagators in gauge theories in presence of a sharp gauge fixing and we apply it to derive the propagators in quantum gravity in the radial gauge, both in the first and in the second order formalism in any space-time dimension. In the three dimensional case such propagators vanish except for singular collinear contributions, in agreement with the absence of propagating gravitons.
General relativity is a covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchar, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or violate the principle of general covariance. In this paper, we explore modifications of general relativity that retain the same number of gravitational degrees of freedom, and therefore explicitly break general covariance. Motivated by cosmology, the modifications of interest maintain spatial covariance. Demanding consistency of the theory forces the physic…
The propagators of the Faddeev-Popov (FP) ghosts for Yang-Mills theories and perturbative quantum gravity in the covariant gauge are infrared (IR) divergent in de Sitter spacetime. We point out, however, that the modes responsible for these divergences will not contribute to loop diagrams in computations of time-ordered products in either Yang-Mills theories or perturbative quantum gravity. Therefore we propose that the IR divergent FP-ghost propagator should be regularized by a small mass term that is sent to zero in the end of any perturbative calculations. This proposal is equivalent to usi…
A covariant gauge independent derivation of the generalized dispersion relation of electromagnetic waves in a medium with local and linear constitutive law is presented. A generalized photon propagator is derived. For Maxwell constitutive tensor, the standard light cone structure and the standard Feynman propagator are reinstated.
Gauge covariance properties of the scalar propagator in spinless/scalar quantum electrodynamics (SQED) are explored in the light of the corresponding Landau-Khalatnikov-Fradkin transformation (LKFT). These transformations are non perturbative in nature and describe how each Green function of the gauge theory changes under a variation of the gauge parameter. With a simple strategy, considering the scalar propagator at the tree level in Landau gauge, we derive a non perturbative expression for this propagator in an arbitrary covariant gauge and three as well as four space-time dimensions. Some r…
We obtain the full 5D graviton propagator in the Randall-Sundrum model with the Gauss-Bonnet interaction. From the decomposition of the graviton propagator on the brane, we show that localization of gravity arises in the presence of the Gauss-Bonnet term. We also obtain the metric perturbation for observers on the brane with considering the brane bending and compute the amplitude of one massless graviton exchange. For the positive definite amplitude or no ghost states, the sign of the Gauss-Bonnet coefficient should be negative in our convention, which is compatible with string amplitude compu…
We reconstruct the Lorentzian graviton propagator in asymptotically safe quantum gravity from Euclidean data. The reconstruction is applied to both the dynamical fluctuation graviton and the background graviton propagator. We prove that the spectral function of the latter necessarily has negative parts similar to, and for the same reasons, as the gluon spectral function. In turn, the spectral function of the dynamical graviton is positive. We argue that the latter enters cross sections and other observables in asymptotically safe quantum gravity. Hence, its positivity may hint at the unitarity…
From first principles, using a screened expansion, a simple one-loop analytical expression is provided for the ghost propagator of pure SU(3) Yang-Mills theory in a generic linear covariant gauge. At variance with the Landau gauge, the ghost dressing function is suppressed in the infrared and vanishes at $p=0$, as predicted by other approaches in the continuum. However, in the very limited range where lattice data are available no detectable deviation is found from the Landau gauge, thus reconciling some recent lattice data and previous continuum predictions.
We evaluate the Wilson loop at second order in general non-covariant gauges by means of the causal principal-value prescription for the gauge- dependent poles in the gauge-boson propagator and show that the result agrees with the usual causal prescriptions.
I consider a simple model where the graviton mass and the cosmological constant depend on a scalar field with appropriate couplings and I calculate the graviton propagator and the resulting effective potential for the scalar field in order to examine issues of stability and symmetry breaking.
We consider the three fundamental one loop Feynman diagrams of QED viz. vertex correction, fermion self-energy and vacuum polarization in the light-front gauge and discuss the equivalence of their standard covariant expressions with the light-front expressions obtained using light-cone time-ordered Hamiltonian perturbation theory. Although this issue has been considered by us and others previously, our emphasis in this article is on addressing the ambiguity regarding the correct form of the gauge boson propagator to be used in the light-front gauge. We generalize our earlier results and show, …
Resumming quantum fluctuations at the level of the gravitational path integral is expected to result in non-local effective actions and thus in a non-trivial momentum dependence of the propagator. Which properties the (dressed) graviton propagator has to satisfy and whether they can all be met are key open questions. In this work we present criteria and conditions for the momentum dependence of a graviton propagator which is consistent with unitarity, causality, and stability in a non-perturbative setting. To this end, we revisit several aspects of these conditions, highlighting some caveats a…
Explicit analytical expressions are derived for the gluon propagator in a generic linear covariant $R_ξ$ gauge, by a screened massive expansion for the exact Faddeev-Popov Lagrangian of pure Yang-Mills theory. At one-loop, if the gauge invariance of the pole structure is enforced, the gluon dressing function is entirely and uniquely determined, without any free parameter or external input. The gluon propagator is found finite in the IR for any $ξ$, with a slight decrease of its limit value when going from the Landau gauge ($ξ=0$) towards the Feynman gauge ($ξ=1$). An excellent agreement is fou…
One loop expressions for fermion self energy,vacuum polarization and vertex correction in light front time ordered perturbation theory (LFTPOT) can be obtained from respective covariant expressions by performing k^- integration. In earlier work, we have shown that the third term in the doubly transverse gauge propagator is necessary to generate the diagrams involving instantaneous photon exchange both in case of fermion self-energy as well as vertex correction.In this work,we show that instantaneous photon exchange diagrams in fermion self-energy as well as th IR singular terms in the propagat…
To reduce general relativity to the canonical Hamiltonian formalism and construct the path (functional) integral in a simpler and, especially in the discrete case, less singular way, one extends the configuration superspace, as in the connection representation. Then we perform functional integration over connection. The module of the result of this integration arises in the leading order of the expansion over a scale of the discrete lapse-shift functions and has maxima at finite (Planck scale) areas/lengths and rapidly decreases at large areas/lengths, as we have mainly considered previously; …
Theories with massive gravitons have peculiarity called the van Dam-Veltman-Zakharov discontinuity in that the massive theory propagator does not go to the massless graviton propagator in the zero graviton mass limit. This results in large deviation in Newtons law for massive graviton theories even when the graviton mass vanishes. We test the vDVZ in massive graviton theories for single graviton vertex process namely the gravitational radiation from a classical source. We calculate the gravitational radiation from compact binaries using the perturbative Feynman diagram method. We perform this …
