Graviton Amplitude Research Articles

Evolution of gravitons in accelerating cosmologies: The case of extended gravity

We discuss the production and evolution of cosmological gravitons showing how the cosmological background affects their dynamics. Besides, the detection of cosmological gravitons could constitute an extremely important signature to discriminate among different cosmological models. Here we consider the cases of scalar-tensor gravity and $f(R)$ gravity where it is demonstrated the amplification of graviton amplitude changes if compared with General Relativity. Possible observational constraints are discussed.

Proving relations between modular graph functions

We consider modular graph functions that arise in the low energy expansion of the four graviton amplitude in type II string theory. The vertices of these graphs are the positions of insertions of vertex operators on the toroidal worldsheet, while the links are the scalar Green functions connecting the vertices. Graphs with four and five links satisfy several non-trivial relations, which have been proved recently. We prove these relations by using elementary properties of Green functions and the details of the graphs. We also prove a relation between modular graph functions with six links.

Non-BPS interactions from the type II one loop four graviton amplitude

We obtain T-duality invariant second order differential equations satisfied by the and interactions from the low energy expansion of the one loop four graviton amplitude in toroidally compactified type II string theory. The eigenvalues of these equations are completely determined by the structure of the one loop integrands. Unlike the BPS interactions, these non-BPS interactions satisfy Poisson equations having source terms that receive contributions from both the bulk and boundary of the worldsheet moduli space. We explicitly solve these equations in nine-dimensions.

Gravitational Compton Scattering from the Worldline Formalism

We report on an ongoing study of photon amplitudes, graviton amplitudes and mixed photon-graviton amplitudes at tree-level using the worldline formalism. We explicitly recalculate the amplitude with one photon and one graviton coupled to a scalar propagator, relevant for graviton photoproduction. We comment on the factorization properties of this amplitude, and outline a generalization to similar processes involving more gravitons.

Some finite terms from ladder diagrams in three and four loop maximal supergravity

We consider the finite part of the leading local interactions in the low energy expansion of the four graviton amplitude from the ladder skeleton diagrams in maximal supergravity on T 2, at three and four loops. At three loops, we express the and amplitudes as integrals over the moduli space of an underlying auxiliary geometry. These amplitudes are evaluated exactly for special values of the the moduli of the auxiliary geometry, where the integrand simplifies. We also perform a similar analysis for the amplitude at four loops that arise from the ladder skeleton diagrams for a special value of a parameter in the moduli space of the auxiliary geometry. While the dependence of the amplitudes on the volume of the T 2 is very simple, the dependence on the complex structure of the T 2 is quite intricate. In some of the cases, the amplitude consists of terms each of which factorizes into a product of two invariant modular forms. While one of the factors is a non-holomorphic Eisenstein series, the other factor splits into a sum of modular forms each of which satisfies a Poisson equation on moduli space with source terms that are bilinear in the Eisenstein series. This leads to several possible perturbative contributions unto genus 5 in type II string theory on S1. Unlike the one and two loop supergravity analysis, these amplitudes also receive non-perturbative contributions from bound states of three D-(anti)instantons in the IIB theory.

Double-soft limits of gluons and gravitons

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 limits yield identical results at the leading order, differences appear at the subleading order. Finally, we discuss double-scalar emission in $$ \mathcal{N}=4 $$ super Yang-Mills theory. These results should be of use in establishing the algebraic structure of potential hidden symmetries in the quantum gravity and Yang-Mills S-matrix.

Graviton amplitudes from collinear limits of gauge amplitudes

We express all tree-level graviton amplitudes in Einstein's gravity as the collinear limits of a linear combination of pure Yang–Mills amplitudes in which each graviton is represented by two gauge bosons, each of them carrying exactly one half of graviton's momentum and helicity.

Pure connection formalism for gravity: recursion relations

In the gauge-theoretic formulation of gravity the cubic vertex becomes simple enough for some graviton scattering amplitudes to be computed using Berends-Giele-type recursion relations. We present such a computation for the current with all same helicity on-shell gravitons. Once the recursion relation is set up and low graviton number cases are worked out, a natural guess for the solution in terms of a sum over trees presents itself readily. The solution can also be described either in terms of the half-soft function familiar from the 1998 paper by Bern, Dixon, Perelstein and Rozowsky or as a matrix determinant similar to one used by Hodges for MHV graviton amplitudes. This solution also immediate suggests the correct guess for the MHV graviton amplitude formula, as is contained in the already mentioned 1998 paper. We also obtain the recursion relation for the off-shell current with all but one same helicity gravitons.

Constraining non-BPS interactions from counterterms in three loop maximal supergravity

The structure of one, two and three loop counterterms imposes strong constraints on several non-BPS interactions in the low momentum expansion of the three loop, four graviton amplitude in maximal supergravity. The constraints are imposed by demanding consistency with string amplitudes. We analyze these constraints imposed on the interaction in 11-dimensional supergravity compactified on T2. We also discuss partial contributions from counterterms to interactions at higher orders in the momentum expansion.

The D6ℛ4 term from three loop maximal supergravity

We consider the term which is the leading contribution in the low momentum expansion of the three loop, four graviton amplitude in maximal supergravity. We calculate the moduli dependent coefficient of this term in eleven dimensional supergravity compactified on T2. Only diagrams that involve the Mercedes skeleton contribute resulting in a compact expression involving an integral over six Schwinger parameters. We express this integral as an integral over the moduli of an auxiliary T3. This includes an invariant integral over the shape moduli of the T3. We discuss the renormalization of the ultraviolet divergences of this amplitude that arise from the boundaries of moduli space. The renormalized amplitude is simple which is a consequence of the fact that the term is Bogomolnyi–Prasad–Sommerfield (BPS).

Low-energy behavior of gluons and gravitons from gauge invariance

We show that at tree level, on-shell gauge invariance can be used to fully determine the first subleading soft-gluon behavior and the first two subleading soft-graviton behaviors. Our proofs of the behaviors for n-gluon and n-graviton tree amplitudes are valid in D dimensions and are similar to Low's proof of universality of the first subleading behavior of photons. In contrast to photons coupling to massive particles, in four dimensions the soft behaviors of gluons and gravitons are corrected by loop effects. We comment on how such corrections arise from this perspective. We also show that loop corrections in graviton amplitudes arising from scalar loops appear only at the second soft subleading order. This case is particularly transparent because it is not entangled with graviton infrared singularities. Our result suggests that if we set aside the issue of infrared singularities, soft-graviton Ward identities of extended BMS symmetry are not anomalous through the first subleading order.

Graviton Scattering Made Simple(r)

I summarize a few recent developments in unlocking the hidden structure of graviton scattering amplitudes. In particular: (1) I show how the 'bonus relations' for graviton amplitudes may be used to provide simple analytic proofs of the equivalence of various distinct formulas for the n-graviton MHV amplitude which have appeared in the literature (and, in particular, providing a direct proof of the original BGK formula); (2) review the 'tree formula' for MHV graviton scattering, which has several nice properties including the fact that it manifests both Sn−2 symmetry as well as 1/z2 falloff at large z; and (3) comment on the solution of the on-shell recursion relation for arbitrary tree-level graviton amplitudes.

Graviton multipoint functions at the AdS boundary

The gauge-gravity duality can be used to relate connected multipoint graviton functions to connected multipoint correlation functions of the stress tensor of a strongly coupled fluid. Here, we show how to construct the connected graviton functions for a particular kinematic regime that is ideal for discriminating between different gravitational theories, in particular between Einstein theory and its leading-order string theory correction. Our analysis begins with the one-particle irreducible graviton amplitudes in an anti-de Sitter black brane background. We show how these can be used to calculate the connected graviton functions and demonstrate that the two types of amplitudes agree in some cases. It is then asserted on physical grounds that this agreement persists in all cases for both Einstein gravity and its leading-order correction. This outcome implies that the corresponding field-theory correlation functions can be read off directly from the bulk Lagrangian, just as can be done for the ratio of the shear viscosity to the entropy density.

On the low-energy limit of one-loop photon–graviton amplitudes

We present first results of a systematic study of the structure of the low-energy limit of the one-loop photon–graviton amplitudes induced by massive scalars and spinors. Our main objective is the search of KLT-type relations where effectively two photons merge into a graviton. We find such a relation at the graviton–photon–photon level. We also derive the diffeomorphism Ward identity for the 1PI one-graviton–N-photon amplitudes.

New recursion relations and a flat space limit for AdS/CFT correlators

We consider correlation functions of the stress-tensor or a conserved current in ${\mathrm{AdS}}_{d+1}/{\mathrm{CFT}}_{d}$ computed using the Hilbert or the Yang-Mills action in the bulk. We introduce new recursion relations to compute these correlators at tree-level. These relations have an advantage over the Britto-Cachazo-Feng-Witten (BCFW)-like relations described in arXiv:1102.4724 and arXiv:1011.0780 because they can be used in all dimensions including $d=3$. We also introduce a new method of extracting flat-space $S$-matrix elements from AdS/CFT correlators in momentum space. We show that the ($d+1$)-dimensional flat-space amplitude of gravitons or gluons can be obtained as the coefficient of a particular singularity of the $d$-dimensional correlator of the stress-tensor or a conserved current; this technique is valid even at loop-level in the bulk. Finally, we show that our recursion relations automatically generate correlators that are consistent with this observation: they have the expected singularity and the flat-space gluon, or graviton amplitude appears as its coefficient.

CONFORMAL INVARIANCE OF TENSOR BOSON TREE AMPLITUDES

The BCFW recursion relation allows to find out the tree-level scattering amplitudes for gluons and tensor gauge bosons in generalized Yang–Mills theory. We demonstrate that the corresponding MHV amplitudes for the tensor gauge bosons of spin-s and n gluons are invariant under conformal group of transformations. This is highly unexpected result for the higher-spin particles, in particular this is not true for the scattering amplitudes of gravitons. We discuss and compare the tree-level scattering amplitudes for the charged tensor bosons with the corresponding scattering amplitudes for gravitons, stressing their differences and similarities.

Tree-level S-matrix elements from S-duality

It has been speculated that the S-matrix elements of type IIB superstring theory satisfy the Ward identity associated with the S-duality. This indicates that a group of S-matrix elements at each loop level are invariant under the linear $SL(2,R)$ transformations. If one evaluates one element of such S-dual multiplet, then all other components can be found by the simple use of the linear $SL(2,R)$ transformations. In this paper, we calculate the disk-level S-matrix element of one graviton(dilaton), one B-field and one gauge boson on the word volume of D$_3$-brane. The S-dual multiplet corresponding to the graviton(dilaton) amplitude has three(six) components. In particular, the graviton multiplet has the S-matrix element of one graviton, one R-R two-form and one gauge boson, and the dilaton multiplet has the S-matrix element of one R-R scalar, one B-field and one gauge boson vertex operators. We calculate explicitly these particular components and show that they are precisely the ones predicted by the S-duality. We have also found the low energy contact terms of the dilaton multiplet at order $\alpha'^2$.

Comments on worldsheet description of the Omega background

Nekrasovʼs partition function is defined on a flat bundle of R 4 over S 1 called the Omega background. When the fibration is self-dual, the partition function is known to be equal to the topological string partition function, which computes scattering amplitudes of self-dual gravitons and graviphotons in type II superstring compactified on a Calabi–Yau manifold. We propose a generalization of this correspondence when the fibration is not necessarily self-dual.

Experimental bounds on large extra dimensions from di-jet event production in hadron collisions

We discuss the new dominant bounds that can be derived on the coefficient of the effective operator generated by tree-level graviton exchange in large extra dimensions from pp → jj data at LHC: MT > 2.1 TeV (ATLAS after 3.1/pb of integrated luminosity), MT > 3.3 TeV (ATLAS after 36/pb of integrated luminosity), MT > 3.4 TeV (CMS after 36/pb). We clarify the role of on-shell graviton exchange and compare the full graviton amplitude to data, setting bounds on the fundamental quantum-gravity scale.

Virtuous trees at five- and six-point levels for Yang-Mills theory and gravity

We present a particularly nice $D$-dimensional graph-based representation of the full color-dressed five-point tree-level gluon amplitude. It possesses the following virtues: (1) it satisfies the color-kinematic correspondence, and thus trivially generates the associated five-point graviton amplitude, (2) all external-state information is encoded in color-ordered partial amplitudes, and (3) one function determines the kinematic contribution of all graphs in the Yang-Mills amplitude, so the associated gravity amplitude is manifestly permutation symmetric. The third virtue, while shared among all known loop-level correspondence-satisfying representations, is novel for tree-level representations sharing the first two virtues. This new $D$-dimensional representation makes contact with the recently found multiloop five-point representations, suggesting all-loop, all-multiplicity ramifications through unitarity. Additionally we present a slightly less virtuous representation of the six-point maximally helicity-violating (MHV) and $\overline{\mathrm{MHV}}$ amplitudes that holds only in four dimensions.