The graviton exchange effect on cosmological correlation functions is examined by employing the double-soft limit technique. A new relation among correlation functions that contain the effects due to graviton exchange diagrams in addition to those due to scalar-exchange and scalar-contact-interaction, is derived by using the background field method and independently by the method of Ward identities associated with dilatation symmetry. We compare these three terms, putting small values for the slow-roll parameters and $(1-n_{s}) = 0.042$, where $n_{s}$ is the scalar spectral index. It is argued that the graviton exchange effects are more dominant than the other two and could be observed in the trispectrum in the double-soft limit. Our observation strengthens the previous work by Seery, Sloth and Vernizzi, in which it has been argued that the graviton exchange dominates in the counter-collinear limit for single field slow-roll inflation.
In this note we explicitly compute the graviton exchange graph for scalar fields with arbitrary conformal dimension Δin arbitrary spacetime dimension d. This results in an analytical function in Δas well as in d.
In arXiv:2008.04330 it was shown that supertranslation and $\overline{SL(2,\mathbb C)}$ current algebra symmetries, corresponding to leading and subleading soft graviton theorems, are enough to determine the tree level MHV graviton scattering amplitudes. In this note we clarify the role of subsubleading soft graviton theorem in this context.
We consider the s-channel scattering of massive fermion or vector-boson pairs with equal helicities, mediated by a graviton in the linearized Einstein theory. We show that, although in general both spin-2 and spin-0 components are present in the exchanged graviton, there is a special set of reference frames where the spin-0 graviton component vanishes. This is connected to the dependence of the trace of the graviton propagator on the effective dimension of the space-time spanned by the sources. On the other hand, one finds a non-vanishing (Lorentz-invariant) interference of the graviton amplit…
The CHY formula which describes an $n$-point tree level scattering amplitude for scalars, gluons or gravitons in arbitrary dimension [22], is used to prove the sub-sub-leading soft- graviton theorem recently proposed by Cachazo and Strominger [13].
We study the soft graviton theorem recently proposed by Cachazo and Strominger. We employ the Cachazo, He and Yuan formalism to show that the next to subleading order soft factor for gravity is universal at tree level in arbitrary dimensions.
We obtain the subleading soft theorem for a generic theory of quantum gravity, for arbitrary number of soft photons and gravitons and for arbitrary number of finite energy particles with arbitrary mass and spin when all the soft particles are soft in the same rate. This result is valid at tree level for spacetime dimensions equal to four and five and to all loops in spacetime dimensions greater than five. We verify that in classical limit low energy photon and graviton radiation decouple from each other.
We extend our investigation of soft graviton effects on the microscopic dynamics of matter fields in de Sitter space. We evaluate the quantum equation of motion in generic gauge theories. We find that the Lorentz invariance can be respected and the velocity of light is not renormalized at the one-loop level. The gauge coupling constant is universally screened by soft gravitons and diminishes with time. These features are in common with other four dimensional field theories with dimensionless couplings. In particular the couplings scale with time with definite scaling exponents. Although indivi…
In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY f…
We show that the recently discovered logarithmic terms in the soft graviton theorem induce a late time component in the gravitational wave-form that falls off as inverse power of time, producing a tail term to the linear memory effect.
We analyze the low-energy behavior of scattering amplitudes involving gravitons at loop level in four dimensions. The single-graviton soft limit is controlled by soft operators which have been argued to separate into a factorized piece and a non-factorizing infrared divergent contribution. In this note we show that the soft operators responsible for the factorized contributions are strongly constrained by gauge and Poincare invariance under the assumption of a local structure. We show that the leading and subleading orders in the soft-momentum expansion can not receive radiative corrections. T…
Extensions of the photon and graviton soft theorems are derived in 4d local effective field theories with massless particles of arbitrary spin. We prove that effective operators can result in new terms in the soft theorems at subleading order for photons and subsubleading order for gravitons. The new soft terms are unique and we provide a complete classification of all local operators responsible for such modifications. We show that no local operators can modify the subleading soft graviton theorem. The soft limits are taken in a manifestly on-locus manner using a complex double deformation of…
The graviton exchange diagram for the correlation function of arbitrary scalar operators is evaluated in anti-de Sitter space, AdS(d+1). This enables us to complete the computation of the 4-point amplitudes of dilaton and axion fields in IIB supergravity on AdS5 X S5. By the AdS/CFT correspondence, we obtain the 4-point functions of the marginal operators Tr (F^2+...) and Tr(F F~ +...) in N=4, d=4 SU(N) SYM at large N, large g^2 N. The short distance asymptotics of the amplitudes are studied. We find that in the direct channel the leading power singularity agrees with the expected contribution…
We present a complete analysis for double soft limit of graviton scattering amplitude using the formalism proposed by Cachazo, He and Yuan. Our results agree with that obtained via BCFW recursion relations in arXiv:1504.05558. In addition we find precise relations between degenerate and nondegenerate solutions of scattering equations with local and nonlocal terms in the soft factor.
In this note we show that the recent conjecture proposed by Cachazo and Strominger holds at tree level in arbitrary dimensions. The proof makes crucial use of the fact that the sub-leading operator is defined using the total angular momentum operator. A key ingredient that makes the proof possible is the CHY formula for graviton amplitudes in arbitrary number of dimensions.
We show that the soft part of the charge generating infinitesimal superrotations can be expressed, in harmonic gauge, in terms of metric components evaluated at the boundaries of null infinity that are subleading in a large radius expansion. We then recast the spin memory observable in terms of these boundary values.
The single-soft-graviton limit of any quantum gravity scattering amplitude is given at leading order by the universal Weinberg pole formula. Gauge invariance of the formula follows from global energy-momentum conservation. In this paper evidence is given for a conjectured universal formula for the finite subleading term in the expansion about the soft limit, whose gauge invariance follows from global angular momentum conservation. The conjecture is non-trivially verified for all tree-level graviton scattering amplitudes using a BCFW recursion relation. One hopes to understand this infinity of …
The scale invariance of the quantum fluctuations in de Sitter space leads to the appearance of de Sitter symmetry breaking infra-red logarithms in the graviton propagator. We investigate physical effects of soft gravitons on the local dynamics of matter fields well inside the cosmological horizon. We show that the IR logarithms do not spoil Lorentz invariance in scalar and Dirac field theory. The leading IR logarithms can be absorbed by a time dependent wave function renormalization factor in the both cases. In the interacting field theory with $λϕ^4$ and Yukawa interaction, we find that the c…
In theories of Einstein gravity coupled with a dilaton and a two-form, a soft theorem for the two-form, known as the Kalb-Ramond B-field, has so far been missing. In this work we fill the gap, and in turn formulate a unified soft theorem valid for gravitons, dilatons and B-fields in any tree-level scattering amplitude involving the three massless states. The new soft theorem is fixed by means of on-shell gauge invariance and enters at the subleading order of the graviton's soft theorem. In contrast to the subsubleading soft behavior of gravitons and dilatons, we show that the soft behavior of …
We derive the subleading soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. Our results are valid to all orders in perturbation theory when the number of non-compact space-time dimensions is six or more, but only for tree amplitudes for five or less non-compact space-time dimensions due to enhanced contribution to loop amplitudes from the infrared region.
We compute the connected four-point correlation function of the primordial curvature perturbation generated during inflation with standard kinetic terms, where the correlation is established via exchange of a graviton between two pairs of scalar fluctuations. Any such correlation yields a contribution to the scalar trispectrum of the order of the tensor to scalar ratio r. This contribution is numerically one order of magnitude larger than the one previously calculated on the basis of scalar perturbations interacting at a point and satisfies a simple relation in the limit where the momentum of …
We compute graviton scattering amplitudes in M-theory using Feynman rules for a scalar particle coupled to gravity in eleven dimensions. The processes that we consider describe the single graviton exchange and the double graviton exchange, that in M(atrix) theory correspond to the $v^4/r^7$- and $v^6/r^{14}$-term respectively. We further show that the $ v^6/r^{14}$-term appearing in M(atrix) theory at two-loops can be obtained from the covariant eleven-dimensional four-graviton amplitude. Finally, we calculate the $v^8/r^{18}$-term appearing at two-loops in M(atrix) theory. It has been previou…
BFSS proposed that asymptotically flat M-theory is dual to a large $N$ limit of the matrix quantum mechanics describing $N$ nonrelativistic D0-branes. Recent insights on the soft symmetries of any quantum theory of gravity in asymptotically flat space are applied to the BFSS matrix model. It is shown that soft gravitons are realized by submatrices whose rank is held fixed in the large $N$ M-theory limit, rather than the usual linear scaling with $N$ for hard gravitons. The soft expansion is identified with the large $N$ expansion and the soft theorem becomes a universal formula for the quantum…
Motivated by the equivalence between soft graviton theorem and Ward identities for the supertranslation symmetries belonging to the BMS group, we propose a new extension (different from the so-called extended BMS) of the BMS group which is a semi-direct product of supertranslations and Diff(S^2). We propose a definition for the canonical generators associated to the smooth diffeomorphisms and show that the resulting Ward identities are equivalent to the subleading soft graviton theorem of Cachazo and Strominger.
Recently, new soft graviton theorem proposed by Cachazo and Strominger has inspired a lot of works. In this note, we use the KLT-formula to investigate the theorem. We have shown how the soft behavior of color ordered Yang-Mills amplitudes can be combined with KLT relation to give the soft behavior of gravity amplitudes. As a byproduct, we find two nontrivial identities of the KLT momentum kernel must hold.
de Sitter corrections to supertranslation Ward identity and soft graviton theorem
School of Physics, The University of Electronic Science and Technology of China（电子科技大学物理学院）；Indian Institute of Information Technology Allahabad (IIITA)（安拉阿巴德信息技术学院）
It is now well understood that Ward identities associated to the (extended) BMS algebra are equivalent to single soft graviton theorems. In this work, we show that if we consider nested Ward identities constructed out of two BMS charges, a class of double soft factorization theorems can be recovered. By making connections with earlier works in the literature, we argue that at the sub-leading order, these double soft graviton theorems are the so-called consecutive double soft graviton theorems. We also show how these nested Ward identities can be understood as Ward identities associated to BMS …
Superstring field theory gives expressions for heterotic and type II string loop amplitudes that are free from ultraviolet and infrared divergences when the number of non-compact space-time dimensions is five or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton. We also prove the leading soft graviton theorem for arbitrary number of finite energy external states and arbitrary number of soft gravitons. Since our analysis is based…
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 …
In a previous article, we have argued that Low's sub-leading soft photon theorem can be recovered as a Ward identity associated to the same large gauge transformations that control the leading piece of the theorem. The key for that was to link the energy expansion displayed in the soft theorem to a $\frac{1}{r}$ expansion that we can perform in the associated asymptotic charge. We expect this idea to be valid in general, and here we provide compelling evidence for it by showing how the same method works in the case of Einstein-Hilbert gravity. More precisely, we are able to derive the three or…
Recently it was conjectured that a certain infinite-dimensional "diagonal" subgroup of BMS supertranslations acting on past and future null infinity (${\mathscr I}^-$ and ${\mathscr I}^+$) is an exact symmetry of the quantum gravity ${\cal S}$-matrix, and an associated Ward identity was derived. In this paper we show that this supertranslation Ward identity is precisely equivalent to Weinberg's soft graviton theorem. Along the way we construct the canonical generators of supertranslations at ${\mathscr I}^\pm$, including the relevant soft graviton contributions. Boundary conditions at the past…
We use insights from superstring field theory to prove the subleading soft graviton theorem for tree amplitudes of (compactified) heterotic and type II string theories for arbitrary number of finite energy NS (NSNS) sector external states but only one soft graviton. We also prove the leading soft graviton theorem in these theories for arbitrary number of external soft gravitons. In our analysis there is no restriction on the mass and spin of the finite energy external states. This method can also be used to give a proof of the subleading soft graviton theorem for tree amplitudes in quantum fie…
We study corrections to the soft graviton theorem at all loop orders in Yukawa and scalar theories, both in the high energy and low energy regions. It is found that the tree level soft theorem is corrected by matrix elements coupled to the Riemann curvature tensor of linearized gravity. Further corrections appear in the high energy region and we develop a power counting technique to classify all such loop corrections according to their order of magnitude. This leads to the construction of factorized contributions to the soft theorem, to which we apply an analysis analogous to Low's theorem bas…
We investigate the relation between the subleading soft graviton theorem and asymptotic symmetries in gravity in even dimensions $d=2+2m$ higher than four. After rewriting the subleading soft graviton theorem as a Ward identity, we argue that the charges of such identity generate Diff$(S^{2m})$. In order to show that, we propose suitable commutation relation among certain components of the metric fields. As a result, all Diff$(S^{2m})$ transformations are symmetries of gravitational scattering.
We analyze scattering amplitudes with one soft external graviton and arbitrary number of other finite energy external states carrying arbitrary mass and spin to sub-subleading order in the momentum of the soft graviton. Our result can be expressed as the sum of a universal part that depends only on the amplitude without the soft graviton and not the other details of the theory and a non-universal part that depends on the amplitude without the soft graviton, and the two and three point functions of the theory. For tree amplitudes our results are valid in all space-time dimensions while for loop…
Classical soft graviton theorem gives an expression for the spectrum of low frequency gravitational radiation, emitted during a classical scattering process, in terms of the trajectories and spin angular momenta of ingoing and outgoing objects, including hard radiation. This has been proved to subleading order in the expansion in powers of frequency by taking the classical limit of the quantum soft graviton theorem. In this paper we give a direct proof of this result by analyzing the classical equations of motion of a generic theory of gravity coupled to interacting matter in space-time dimens…
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 sugg…
The double-soft limit of gluon and graviton amplitudes is studied in four dimensions at tree level. In general this limit is ambiguous and we introduce two natural ways of taking it: A consecutive double-soft limit where one particle is taken soft before the other and a simultaneous limit where both particles are taken soft uniformly. All limits yield universal factorisation formulae which we establish by BCFW recursion relations down to the subleading order in the soft momentum expansion. These formulae generalise the recently discussed subleading single-soft theorems. While both types of lim…
Classical soft photon and soft graviton theorems determine long wavelength electromagnetic and gravitational waveforms for a general classical scattering process in terms of the electric charges and asymptotic momenta of the ingoing and outgoing macroscopic objects. Performing Fourier transformation of the electromagnetic and gravitational waveforms in the frequency variable one finds electromagnetic and gravitational waveforms at late and early retarded time. Here extending the formalism developed in \cite{1912.06413}, we derive sub-subleading electromagnetic and gravitational waveforms which…
It is well-known that there exists a close relation between a large $N$ matrix model and noncommutative (NC) field theory: The latter can be naturally obtained from the former by expanding it around a specific background. Because the matrix model can be a constructive formulation of string theory, this relation suggests that NC field theory can also include quantum gravity. In particular, the NC $U(1)$ gauge theory attracts much attention because its low-energy effective action partially contains gravity where the metric is determined by the $U(1)$ gauge field. Thus, the NC $U(1)$ gauge theory…
In this contribution we present results of the calculations of several hadronic spectra within the holographic graviton soft-wall (GSW) model. In particular, we studied and compared with data for the ground state and excitations of: glueballs, scalar, vector, axial and pseudo-scalar mesons. The GSW model is found to be capable to describe these observable with only few parameters.
We study the imprint of a massive scalar particle on cosmological correlation functions, and suggest the way to determine the mass of the newly introduced particle, which is expected to be around 10^14 GeV. After reviewing the basic theory by Maldacena and the effective field theory (EFT) of inflation by Cheung et al., we apply these two theories to construct new couplings of a massive scalar field with primordial fluctuations including an arbitrary number of gravitons. We compute some correlation functions including these couplings in the soft-graviton limit. We show that when the number of s…
Graviton mediated polarisation-polarisation entanglement of photons by means of the Schwinger Keldysh and Kadanoff Baym formalisms and Quantum Boltzmann equations
We apply recently developed path integral resummation methods to perturbative quantum gravity. In particular, we provide supporting evidence that eikonal graviton amplitudes factorize into hard and soft parts, and confirm a recent hypothesis that soft gravitons are modelled by vacuum expectation values of products of certain Wilson line operators, which differ for massless and massive particles. We also investigate terms which break this factorization, and find that they are subleading with respect to the eikonal amplitude. The results may help in understanding the connections between gravity …
We study all translationally and rotationally invariant local theories involving massless spin 2 and spin 1 particles that mediate long range forces, allowing for general energy relations and violation of boost invariance. Although gauge invariance is not a priori required to describe non Lorentz invariant theories, we first establish that locality requires `soft gauge invariance'. Then by taking the soft graviton limit in scattering amplitudes, we prove that in addition to the usual requirement of universal graviton couplings, the special relativistic energy-momentum relation is also required…
We discuss how scattering amplitudes in 4d Minkowski spacetime which involve multiple soft gravitons realize the algebra of BMS charges on the null boundary. In particular, we show how the commutator of two such charges is realized by the antisymmetrized consecutive soft limit of the double soft amplitude. The commutator is found to be robust even in the presence of quantum corrections, and the associated Lie algebra has an extension, which breaks the BMS symmetry if the BMS algebra is taken to include the Virasoro algebra of local superrotations. We discuss the implications of this structure …
Classical subleading soft graviton theorem in four space-time dimensions determines the gravitational wave-form at late and early retarded time, generated during a scattering or explosion, in terms of the four momenta of the ingoing and outgoing objects. This result was `derived' earlier by taking the classical limit of the quantum soft graviton theorem, and making some assumptions about how to deal with the infrared divergences of the soft factor. In this paper we give a direct proof of this result by analyzing the classical equations of motion of gravity coupled to matter. We also extend the…
An asymptotic proof of the classical log soft graviton theorem
Instituto de Física, Facultad de Ingeniería, Universidad de la República（乌拉圭共和国大学工程学院物理研究所）；Instituto de Física, Facultad de Ciencias, Universidad de la República（乌拉圭共和国大学理学院物理研究所）
We construct an expression for the n-point one-loop graviton scattering amplitude with a single negative helicity external leg using an augmented recursion technique. We analyse the soft-limits of these amplitudes and demonstrate that they have soft behaviour beyond the conjectured universal behaviour.
We construct, in the closed bosonic string, the multiloop amplitude involving $N$ tachyons and one massless particle with $26 -D$ compactified directions, and we show that at least for $D>4$, the soft behaviors of the graviton and dilaton satisfy the same soft theorems as at the tree level, up to one additional term at the subsubleading order, which can only contribute to the dilaton soft behavior and which we show is zero at least at one loop. This is possible, since the infrared divergences due to the non-vanishing tachyon and dilaton tadpoles do not depend on the number of external particle…
In the sea of super-strong interacting gravitons, non-forehead collisions with gravitons deflect photons, and this deflection may differ for soft and hard radiations. As a result, the Hubble diagram would not be a universal function and it will have a different view for such sources as supernovae in visible light and gamma-ray bursts. Observations of these two kinds are compared here with the limit cases of the Hubble diagram.
