We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multiloop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the KLT relations between gauge and gravity tree amplitudes. This can be used to obtain novel relations similar to the KLT ones. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.

In a previous paper we observed that (classical) tree-level gauge theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N = 4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N = 8 supergravity. We also remark on a non-supersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an anti-symmetric tensor and dilaton.PACS numbers: 04.65.+e, 11.15. Bt, 11.25.Db, 12.60.Jv Although gauge and gravity theories have rather different physical behaviors we know that they are intimately linked. The celebrated AdS/CFT correspondence [1] is the most striking such example, linking maximally supersymmetric gauge theory to supergravity in AdS space. We also know that at weak coupling the tree-level (classical) scattering amplitudes of gauge and gravity theories are deeply intertwined because of the Kawai, Lewellen and Tye (KLT) relations [2].Recent years have seen a renaissance in the study of scattering amplitudes driven in part by the resurgence of collider physics with the recent start up of the Large Hadron Collider at CERN and by the realization that scattering amplitudes have far simpler and richer structures than visible from Feynman diagrams. Striking examples are the discoveries of twistor-space [3] and Grassmannian structures [4] in four dimensions for N = 4 super-Yang-Mills (sYM) theory, as well as interpolations between weak and strong coupling [5][6][7]. In another development we noted [8] that at tree level we could impose a duality between color and kinematics for gauge theories, without altering the amplitudes. This has important consequences in clarifying the tree-level relation between gravity and gauge theory. As we shall argue this duality also greatly clarifies the multiloop structure of (super)gravity theories.The key tool for our studies of loop amplitudes has been the unitarity method [9]. An important refinement which simplifies multiloop studies is the method of maximal cuts [10,11], which relies on generalized unitarity [12]. Here we will make use of these tools to present an all-loop extension of recently discovered tree-level relations. As we shall explain, this allows us to immediately write down multiloop gravity amplitudes directly from gauge-theory multiloop amplitudes once they have been organized to respect the duality between kinematics and color.To understand the relationship between tree-level gravity and gauge theory amplitudes, consider a gauge-theory amplitude where all particles are in the adjoint color representation. By exercising the trivial ability to absorb...

Large scale structure surveys will likely become the next leading cosmological probe. In our universe, matter perturbations are large on short distances and small at long scales, i.e. strongly coupled in the UV and weakly coupled in the IR. To make precise analytical predictions on large scales, we develop an effective field theory formulated in terms of an IR effective fluid characterized by several parameters, such as speed of sound and viscosity. These parameters, determined by the UV physics described by the Boltzmann equation, are measured from N -body simulations. We find that the speed of sound of the effective fluid is c 2 s ≈ 10 −6 c 2 and that the viscosity contributions are of the same order. The fluid describes all the relevant physics at long scales k and permits a manifestly convergent perturbative expansion in the size of the matter perturbations δ(k) for all the observables. As an example, we calculate the correction to the power spectrum at order δ(k) 4 . The predictions of the effective field theory are found to be in much better agreement with observation than standard cosmological perturbation theory, already reaching percent precision at this order up to a relatively short scale k 0.24h Mpc −1 .

Large scale structure surveys promise to be the next leading probe of cosmological information. It is therefore crucial to reliably predict their observables. The Effective Field Theory of Large Scale Structures (EFTofLSS) provides a manifestly convergent perturbation theory for the weakly non-linear regime of dark matter, where correlation functions are computed in an expansion of the wavenumber k of a mode over the wavenumber associated with the non-linear scale k NL . Since most of the information is contained at high wavenumbers, it is necessary to compute higher order corrections to correlation functions. After the one-loop correction to the matter power spectrum, we estimate that the next leading one is the two-loop contribution, which we compute here. At this order in k/k NL , there is only one counterterm in the EFTofLSS that must be included, though this term contributes both at tree-level and in several one-loop diagrams. We also discuss correlation functions involving the velocity and momentum fields. We find that the EFTofLSS prediction at two loops matches to percent accuracy the non-linear matter power spectrum at redshift zero up to k ∼ 0.6 h Mpc −1 , requiring just one unknown coefficient that needs to be fit to observations. Given that Standard Perturbation Theory stops converging at redshift zero at k ∼ 0.1 h Mpc −1 , our results demonstrate the possibility of accessing a factor of order 200 more dark matter quasi-linear modes than naively expected. If the remaining observational challenges to accessing these modes can be addressed with similar success, our results show that there is tremendous potential for large scale structure surveys to explore the primordial universe.

We present an Ansatz for the planar five-loop four-point amplitude in maximally supersymmetric YangMills theory in terms of loop integrals. This Ansatz exploits the recently observed correspondence between integrals with simple conformal properties and those found in the four-point amplitudes of the theory through four loops. We explain how to identify all such integrals systematically. We make use of generalized unitarity in both four and D dimensions to determine the coefficients of each of these integrals in the amplitude. Maximal cuts, in which we cut all propagators of a given integral, are an especially effective means for determining these coefficients. The set of integrals and coefficients determined here will be useful for computing the five-loop cusp anomalous dimension of the theory which is of interest for nontrivial checks of the AdS/CFT duality conjecture. It will also be useful for checking a conjecture that the amplitudes have an iterative structure allowing for their all-loop resummation, whose link to a recent string-side computation by Alday and Maldacena opens a new venue for quantitative AdS/CFT comparisons.