We formulate Positivity Bounds for scattering amplitudes including exchange of massless particles. We generalize the standard construction through dispersion relations to include the presence of a branch cut along the real axis in the complex plane for the Maldestam variable $s$. In general, validity of these bounds require the cancellation of divergences in the forward limit of the amplitude, proportional to $t^{-1}$ and $\log(t)$. We show that this is possible in the case of gravitons if one assumes a Regge behavior of the amplitude at high energies below the Planck scale, as previously suggested in the literature, and that the concrete UV behaviour of the amplitude is uniquely determined by the structure of IR divergences. We thus extend previous results by including a sub-leading logarithmic term, which we show to be universal. The bounds that we present here have the potential of constraining very general models of modified gravity and EFTs of matter coupled to gravitation.
Scattering amplitudes mediated by graviton exchange display IR singularities in the forward limit. This obstructs standard application of positivity bounds based on twice subtracted dispersion relations. Such divergences can be cancelled only if the UV limit of the scattering amplitude behaves in a specific way, which implies a very non-trivial connection between the UV and IR behaviors of the amplitude. We show that this relation can be expressed in terms of an integral transform, obtaining analytic results when $t \log{s}\rightarrow 0$. Carefully applying this limit to dispersion relations, …
We show that a partially massless graviton can propagate on a large set of spacetimes which are not Einstein spacetimes. Starting from a recently constructed theory for a massive graviton that propagates the correct number of degrees of freedom on an arbitrary spacetime, we first give the full explicit form of the scalar constraint responsible for the absence of a sixth degree of freedom. We then spell out generic conditions for the constraint to be identically satisfied, so that there is a scalar gauge symmetry which makes the graviton partially massless. These simplify if one assumes that sp…
We use a simplified formalism to re-compute the single graviton loop contribution to the self-mass of a massless, conformally coupled scalar on de Sitter background which was originally made by Boran, Kahya and Park [1-3]. Our result resolves the problem with the flat space correspondence limit that was pointed out by Fröb [4]. We discuss how this computation will be used in a long-term project to purge the linearized effective field equation of gauge dependence.
We study the constraint structure of Fierz -Pauli action in both flat and curved space in the framework of Hamiltonian formalism. We observe an abrupt change in the constraint algebra and the characteristics of the constraints when the mass term is turned off. As is well-known, for de Sitter background with a special tuning of the mass, we will have a gauge symmetry and one degree of freedom less. We will show how this abrupt change in the behavior of the system is reflected on the properties of the constraint algebra. We also obtain the generating functional of gauge transformations both for …
In the holographic picture, the Brout-Englert-Higgs (BEH) mechanism in d-dimensional Yang-Mills theories is conjectured to provide a Higgs-like mechanism for gravity in d+1 dimensions, resulting in massive (or massless) gravitons in IR (or UV) completions. Accordingly, one could imagine dual (magnetic-type) fields of massive gravitons in the IR (low-energy) limit that are coupled to the curl of their own energy-momentum, as well as to the rotation of matter fields on large scales. This hypothesis, which might solve cosmological issues currently ascribed to dark matter and dark energy, needs to…
We study a novel class of higher derivative theories for interacting massless gravitons in Minkowski spacetime. These theories were first discussed by Wald decades ago, and are characterized by scattering amplitudes essentially different from general relativity and many of its modifications. We discuss various aspects of these higher derivative theories, including the Lagrangian construction, violation of asymptotic causality, scattering amplitudes, non-renormalization, and possible implications on emergent gravitons from condensed matter systems.
We construct an n-dimensional Born-Infeld type gravity theory that has the same properties as Einstein's gravity in terms of the vacuum and particle content: Namely, the theory has a unique viable vacuum (maximally symmetric solution) and a single massless unitary spin-2 graviton about this vacuum. The BI gravity, in some sense, is the most natural, minimal generalization of Einstein's gravity with a better UV behavior, and hence, is a potentially viable proposal for low energy quantum gravity. The Gauss-Bonnet combination plays a non-trivial role in the construction of the theory. As an extre…
We construct Born-Infeld (BI) type gravity theories which describe tree-level unitary (non-ghost and non-tachyonic) massless spin-2 modes around their maximally symmetric vacua in four dimensions. Building unitary BI actions around flat vacuum is straightforward; but, this is a complicated task around (anti)-de Sitter backgrounds. In this work, we solve the issue and give details of constructing perturbatively viable determinantal BI theories. It is interesting that the Gauss-Bonnet combination, which is a total derivative in four dimensions, plays an important role in the construction of viab…
We provide a unified treatment of electric-magnetic duality, at the action level and with manifest Lorentz invariance, for massive, massless as well as partially-massless gravitons propagating in maximally symmetric spacetimes of any dimension n>3. For massive and massless fields, we complete previous analyses that use parent-action techniques by giving dual descriptions that enable direct counting of physical degrees of freedom in the flat and massless limit. The same treatment is extended to the partially-massless case, where the duality has been previously discussed in covariant form only a…
We consider a braneworld model in which an anisotropic brane is embedded in a dilatonic background. We solve the background solutions and study the behavior of the perturbations when the universe evolves from an inflationary Kasner phase to a Minkowski phase. We calculate the massless mode spectrum, and find that it does not differ from what expected in standard four-dimensional cosmological models. We then evaluate the spectrum of both light (ultrarelativistic) and heavy (nonrelativistic) massive modes, and find that, at high energies, there can be a strong enhancement of the Kaluza-Klein spe…
Under the hypotheses of smoothness of the interactions in the coupling constant, locality, Poincare invariance, Lorentz covariance, and the preservation of the number of derivatives on each field in the Lagrangian of the interacting theory (the same number of derivatives like in the free Lagrangian), we prove that in D=11 there are no cross-interactions between the graviton and the massless gravitino and also no self-interactions in the Rarita-Schwinger sector. A comparison with the case D=4 is briefly discussed.
We point out that it is possible to define CFT duals to AdS theories with massive gravitons only. This is achieved by considering the product of two or more CFTs on the boundary, each possessing a large-N expansion and a corresponding bulk dual. It is possible to couple the CFTs through a marginal perturbation that makes all but one of the bulk gravitons massive. In the infinite-N limit for one of the CFTs the massless graviton decouples.
The striking GW170817 event indicated that the graviton is nearly massless, since the gamma rays emitted from the two neutron stars merging arrived almost simultaneously with the gravitational waves. Thus, the graviton must also be massless during the inflationary and post-inflationary era, since there is no obvious reason to believe otherwise. In this letter we shall investigate the theoretical implications of the constraint that the graviton is massless to an Einstein-Gauss-Bonnet theory with linear coupling of the scalar field to the four dimensional Gauss-Bonnet invariant. As we show, the …
Under the hypotheses of smoothness of the interactions in the coupling constant, locality, Poincare invariance, Lorentz covariance, and the preservation of the number of derivatives on each field in the Lagrangian of the interacting theory (the same number of derivatives like in the free Lagrangian), we prove that the only consistent interactions in D=11 among massless gravitini, a graviton, and a 3-form are described by N=1, D=11 SUGRA.
The couplings that can be introduced between a massless Rarita-Schwinger field, a Pauli-Fierz field and an Abelian three-form gauge field in eleven spacetime dimensions are analyzed in the context of the deformation of the solution of the master equation.
We discuss the possibility of localizing Einstein gravity on a three-brane embedded in a five-dimensional Minkowski space by giving a space-dependent mass to the graviton. We show that, with an overall fine tuning of the mass profile, it is possible to localize a massless graviton with a finite mass gap from the massive Kaluza-Klein modes. The theory does not contain ghosts and no scalar massless mode is sourced by brane matter. A massless vector mode is strongly coupled to the flux of energy-momentum into the extra dimension, so that it is not sourced as long as only brane-localized matter is…
We review some recent work by Carone, Erlich and Vaman on composite gravitons in metric-independent quantum field theories, with the aim of clarifying a number of basic issues. Focusing on a theory of scalar fields presented previously in the literature, we clarify the meaning of the tunings required to obtain a massless graviton. We argue that this formulation can be interpreted as the massless limit of a theory of massive composite gravitons in which the graviton mass term is not of Pauli-Fierz form. We then suggest closely related theories that can be defined without such a limiting procedu…
Recent nonlinear completions of Fierz-Pauli theory for a massive spin-2 field include nonlinear massive gravity and bimetric theories. The spectrum of black-hole solutions in these theories is rich, and comprises the same vacuum solutions of Einstein's gravity enlarged to include a cosmological constant. It was recently shown that Schwarzschild (de Sitter) black holes in these theories are generically unstable against spherical perturbations. Here we show that a notable exception is partially massless gravity, where the mass of the graviton is fixed in terms of the cosmological constant by μ^2…
The proof of the fact that there are no nontrivial, consistent cross-couplings that can be added between the Weyl graviton and the massless Rarita-Schwinger field is accomplished by means of a cohomological approach, based on the deformation of the solution to the master equation from the antifield-Becchi-Rouet-Stora-Tyutin (BRST) formalism. The procedure developed here relies on the assumptions of locality, smoothness, (background) Lorentz invariance, Poincare invariance, and preservation of the number of derivatives with respect to each field (the last hypothesis was made only in antighost n…
Cross-couplings between a massless spin-two field (described in the free limit by the Pauli-Fierz action) and an Abelian three-form gauge field in D=11 are investigated in the framework of the deformation theory based on local BRST cohomology. These consistent interactions are obtained on the grounds of smoothness in the coupling constant, locality, Lorentz covariance, Poincare invariance, and the presence of at most two derivatives in the interacting Lagrangian. Our results confirm the uniqueness of the eleven-dimensional interactions between a graviton and a three-form prescribed by General …
We investigate the conditions for obtaining four-dimensional massless spin-2 states in the spectrum of fluctuations around an asymptotically $AdS_5$ solution of Einstein-Dilaton gravity. We find it is only possible to have normalizable massless spin-2 modes if the space-time terminates at some IR point in the extra dimension, far from the UV AdS boundary, and if suitable boundary conditions are imposed at the ``end of space.'' In some of these cases the 4D spectrum consists only of a massless spin-2 graviton, with no additional massless or light scalar or vector modes. These spin-2 modes have …
We study the extensions of DGP model which are described by five-dimensional Einstein gravity coupled covariantly to 3-brane with induced gravity term and consider warped D=4 de Sitter background field solutions on the brane. The case with included D=5 AdS cosmological term is also considered. Following background field method we obtain the field equations described by the Lagrangean terms bilinear in gravitational field. In such a linear field approximation on curved dS background we calculate explicitly the five-dimensional massive terms as well as the mass-like ones on the brane. We investi…
We relax the assumption of time translation and Lorentz boost symmetry in theories involving massless spin 2 gravitons, while maintaining a basic notion of locality that there is no instantaneous signaling at a distance. We project out longitudinal modes, leaving only two degrees of freedom of the graviton. Our previous work, which assumed time translation symmetry, found that the Lorentz boost symmetry is required to ensure locality at leading order. In this work, without assuming time translations or Lorentz boosts, we show that locality of the exchange action between matter sources demands …
Classical soft graviton theorem gives the gravitational wave-form at future null infinity at late retarded time $u$ for a general classical scattering. The large $u$ expansion has three known universal terms: the constant term, the term proportional to $1/u$ and the term proportional to $\ln u/u^2$, whose coefficients are determined solely in terms of the momenta of incoming and the outgoing hard particles, including the momenta carried by outgoing gravitational and electromagnetic radiation produced during scattering. For the constant term, also known as the memory effect, the dependence on t…
We show that higher spin systems specific to cosmological spaces are subject to the same problems as models with Poincar'e limits. In particular, we analyse partially massless (PM) spin 2 and find that both its gravitational coupling and nonlinear extensions suffer from the usual [background- and self-coupling] difficulties: Consistent free field propagation does not extend beyond background Einstein geometries. Then, using conformal Weyl gravity (CG), which consists of relative ghost PM and graviton excitations, we find that avoiding graviton-ghosts restricts CG-generated PM self-couplings to…
Non-linear partially massless (PM) gravity, if it exists, is a theory of massive gravity in which the graviton has four propagating degrees of freedom. In PM gravity, a scalar gauge symmetry removes one of the five modes of the massive graviton. This symmetry ties the value of the cosmological constant to the mass of the graviton, which in turn can be kept small in a technically natural way. Thus PM gravity could offer a compelling solution to the old cosmological constant problem. In this work we look for such a theory among the known ghost-free massive gravity models with a de Sitter referen…
The graviton localized on the 3-brane is examined in Randall-Sundrum brane-world scenario from the viewpoint of one-dimensional singular quantum mechanics. For the Randall-Sundrum single brane scenario the one-parameter family of the fixed-energy amplitude is explicitly computed where the free parameter $ξ$ parametrizes the various boundary conditions at the brane. The general criterion for the localized graviton to be massless is derived when $ξ$ is arbitrary but non-zero. When $ξ=0$, the massless graviton is obtained via a coupling constant renormalization. For the two branes picture the fix…
We discuss the cosmological amplification of tensor perturbations in a simple example of brane-world scenario, in which massless gravitons are localized on a higher-dimensional Kasner-like brane embedded in a bulk AdS background. Particular attention is paid to the canonical normalization of the quadratic action describing the massless and massive vacuum quantum fluctuations, and to the exact mass-dependence of the amplitude of massive fluctuations on the brane. The perturbation equations can be separated. In contrast to de Sitter models of brane inflation, we find no mass gap in the spectrum …
The presence of a massless spin-2 field in an effective field theory results in a $t$-channel pole in the scattering amplitudes that precludes the application of standard positivity bounds. Despite this, recent arguments based on compactification to three dimensions have suggested that positivity bounds may be applied to the $t$-channel pole subtracted amplitude. If correct this would have deep implications for UV physics and the Weak Gravity Conjecture. Within the context of a simple renormalizable field theory coupled to gravity we find that applying these arguments would constrain the low-e…
In this work we shall introduce a theoretical framework comprised by a non-minimal coupled canonical scalar field, a non-minimal coupling to the Gauss-Bonnet invariant and a non-minimal kinetic coupling. This theoretical framework is basically a non-minimally coupled Einstein-Gauss-Bonnet theory with extra corrections of the form of a non-minimal kinetic coupling. In order to comply with the GW170817 event, we shall impose a constraint on the propagation speed of the primordial tensor perturbations that it is equal to that of light's in vacuum, and this constraint basically specifies the way t…
We show that the mixed gravitational/gauge superstring amplitudes describing decays of massless closed strings - gravitons or dilatons - into a number of gauge bosons, can be written at the tree (disk) level as linear combinations of pure open string amplitudes in which the graviton (or dilaton) is replaced by a pair of collinear gauge bosons. Each of the constituent gauge bosons carry exactly one half of the original closed string momentum, while their +/- 1 helicities add up to +/- 2 for the graviton or to 0 for the dilaton.
We calculate the quark self-energy at one-loop level at high temperature, taking into account contributions from both the (chromo)electric scale $gT$ and the (chromo)magnetic scale $g^2T$. While reproducing standard massive excitations due to the electric scale, we uncover a novel massless excitation ascribable to the magnetic scale. The residue of this massless excitation is nonpositive at all temperatures, which consequently gives rise to positivity violation in the quark spectral functions. This demonstrates the profound impact of confinement effects on thermal quark collective excitations,…
The massive spin-2 quantum gauge theory previously developed is applied to calculate gravitational bremsstrahlung. It is shown that this theory is unique and free from defects. In particular, there is no strong coupling if the graviton mass becomes small. The cross sections go over smoothly into the ones of the massless theory in the limit of vanishing graviton mass. The massless cross sections are calculated for the full tensor theory.
We study the validity of positivity bounds in the presence of a massless graviton, assuming the Regge behavior of the amplitude. Under this assumption, the problematic $t$-channel pole is canceled with the UV integral of the imaginary part of the amplitude in the dispersion relation, which gives rise to finite corrections to the positivity bounds. We find that low-energy effective field theories (EFT) with "wrong" sign are generically allowed. The allowed amount of the positivity violation is determined by the Regge behavior. This violation is suppressed by $M_{\rm pl}^{-2}α'$ where $α'$ is th…
We formulate a theory of gravity with a matrix-valued complex vierbein based on the SL(2N,C)xSL(2N,C) gauge symmetry. The theory is metric independent, and before symmetry breaking all fields are massless. The symmetry is broken spontaneously and all gravitons corresponding to the broken generators acquire masses. If the symmetry is broken to SL(2,C) then the spectrum would correspond to one massless graviton coupled to $2N^2 -1$ massive gravitons. A novel feature is the way the fields corresponding to non-compact generators acquire kinetic energies with correct signs. Equally surprising is th…
The interactions that can be introduced between a massless Rarita-Schwinger field and an Abelian three-form gauge field in eleven spacetime dimensions are analyzed in the context of the deformation of the free solution of the master equation combined with local BRST cohomology. Under the hypotheses of smoothness of the interactions in the coupling constant, locality, Poincare invariance, Lorentz covariance, and the presence of at most two derivatives in the Lagrangian of the interacting theory (the same number of derivatives like in the free Lagrangian), we prove that there are neither cross-c…
We obtain the equation that describe the conditions of quantization for neutral massless bosons on an arbitrary curved space-time, obtained using a particular theoretical formalism developed in a previous work\cite{MM}. In particular, we study the emission of neutral massless $(1, 2)\hbar$-spin bosons during pre-inflation using the recently introduced unified spinor field theory. We conclude that during pre-inflation (which is governed by an vacuum equation of state), is emitted gravitational radiation, which could be detected in the future, as primordial gravitational radiation.
We calculate the one loop graviton vacuum polarization induced by a massless, nonminimally coupled scalar field on Minkowski background. We make use of the Schwinger-Keldysh formalism, which allows us to study time dependent phenomena. As an application we compute the leading quantum correction to the Newtonian potential of a point particle. The novel aspect of the calculation is the use of the Schwinger-Keldysh formalism, within which we calculate the time transients induced by switching on of the graviton-scalar coupling.
We study the behavior of the scattering amplitudes of the bosonic string involving a soft massless state (graviton, dilaton and Kalb-Ramond antisymmetric tensor) and closed string tachyons or other closed string massless states. For a soft graviton we confirm the results, obtained in Ref. [24] using just gauge invariance, up to terms of ${\cal O}(q^1)$ for external tachyons and up to terms of ${\cal O} (q^0)$ for external massless closed string states. Furthermore, we also derive the behavior of the scattering amplitude when a dilaton or a Kalb-Ramond field becomes soft. These results are new …
The extended-BMS algebra of asymptotically flat spacetime contains an SO(3,1) subgroup that acts by conformal transformations on the celestial sphere. It is of interest to study the representations of this subgroup associated with gravitons. To reduce the equation of motion to a Schrodinger-like equation it is necessary to impose a non-covariant gauge condition. Using these solutions, leading-order gauge invariant Weyl scalars are then computed and decomposed into families of unitary principal series representations. An invertible holographic mapping is constructed between these unitary princi…
We solve the effective Dirac equation for massless fermions during inflation in the simplest gauge, including all one loop corrections from quantum gravity. At late times the result for a spatial plane wave behaves as if the classical solution were subjected to a time dependent field strength renormalization of Z_2(t) = 1 - \frac{17}{4 π} G H^2 \ln(a) + O(G^2). We show that this also follows from making the Hartree approximation, although the numerical coefficients differ.
We derive the kinematical constraints which characterize the decay of any massless particle in flat spacetime. We show that in perturbation theory the decay probabilities of photons and Yang-Mills bosons vanish to all orders; the decay probability of the graviton vanishes to one-loop order for graviton loops and to all orders for matter loops. A general power counting argument indicates in which conditions a decay of a massless particle could be possible: the lagrangian should contain a self-coupling without derivatives and with a coupling constant of positive mass dimension.
Instituto de Física Teórica UAM/CSIC（马德里自治大学/西班牙国家研究委员会理论物理研究所）；Leinweber Institute for Theoretical Physics at Stanford, Department of Physics, Stanford University（斯坦福大学莱因韦伯理论物理研究所物理系）
We use the feature that the gravitational Compton scattering amplitude factorizes in terms of Abelian QED amplitudes to evaluate various gravitational Compton processes. We examine both the QED and gravitational Compton scattering from a massive spin-1 system by the use of helicity amplitude methods. In the case of gravitational Compton scattering we show how the massless limit can be used to evaluate the cross section for graviton-photon scattering and discuss the difference between photon interactions and the zero mass spin-1 limit. We show that the forward scattering cross section for gravi…
We study the bending of gravitons that pass near a massive object like the Sun, using scattering amplitudes in which the Sun is represented by a massive scalar particle. Our results complete previous work on the bending angles of massless spin-0, spin-$\frac{1}{2}$ and spin-1 particles, and provides more evidence for the violation of the equivalence principle at the quantum level, in the sense that the quantum corrections to bending angles for massless particles with different spins are different. We provide a universal expression for the bending angle in terms of coefficients of triangle and …
We derive new positivity bounds for scattering amplitudes in theories with a massless graviton in the spectrum in four spacetime dimensions, of relevance for the weak gravity conjecture and modified gravity theories. The bounds imply that extremal black holes are self-repulsive, $M/|Q|<1$ in suitable units, and that they are unstable to decay to smaller extremal black holes, providing an S-matrix proof of the weak gravity conjecture. We also present other applications of our bounds to the effective field theory of axions, $P(X)$ theories, weakly broken galileons, and curved spacetimes.
A new mechanism which leads to a linearized massless graviton localized on the brane is found in the $AdS$/CFT setting, {\it i.e.} in a single copy of $AdS_5$ spacetime with a singular brane on the boundary, within the Randall-Sundrum brane-world scenario. With an help of a recent development in path-integral techniques, a one-parameter family of propagators for linearized gravity is obtained analytically, in which a parameter $ξ$ reflects various kinds of boundary conditions that arise as a result of the half-line constraint. In the case of a Dirichlet boundary condition ($ξ= 0$) the graviton…
