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Applying the quantum field theoretic perturbiner approach to Einstein gravity, we compute the metric of a Schwarzschild black hole order by order in perturbation theory. Using recursion, this calculation can be carried out in de Donder gauge to all orders in Newton's constant. The result is a geometric series which is convergent outside a disk of finite radius, and it agrees within its region of convergence with the known de Donder gauge metric of a Schwarzschild black hole. It thus provides a first all-order perturbative computation in Einstein gravity with a matter source, and this series converges to the known non-perturbative expression in the expected range of convergence., Comment: 7 pages, no figure; v2: references added; v3: one reference added, version to appear in Physical Review Letters

By combining the KMOC-formalism with the exponential representation of the scattering matrix we show that the two-body scattering angle is given by the corresponding matrix element of the exponential representation. This holds to all orders in the Post-Minkowskian expansion of gravity when restricted to the conservative sector. Once gravitational radiation is taken into account new terms correcting this relationship appear starting at fourth Post-Minkowskian order. A systematic expansion of the momentum kick is provided to any order, thus illustrating the iterative structure that partly recycles terms from lower orders in the Post-Minkowskian expansion. We provide explicit results for this computation to fourth Post-Minkowskian order, the first complete calculation at this order based on scattering amplitudes., Comment: 37 pages. v2 : Misprints corrected, text edited, results unchanged

We demonstrate the equivalence between KMOC and worldline formalisms for classical general relativity, highlighting how the Keldysh-Schwinger in-in formalism is contained in both of them even though the KMOC representation conventionally leads to the evaluation of scattering amplitudes with Feynman propagators. The relationship between the two approaches is illustrated in detail for the momentum kick at second Post-Minkowskian order., Comment: 39 pages. v2: Some clarifications and references added. Version to appear in JHEP

Scattering angles for probes in Kerr metrics are derived for scattering in the equatorial plane of the black hole. We use a method that naturally resums all orders in the spin of the Kerr black hole, thus facilitating comparisons with scattering-angle computations based on the Post-Minkowskian expansion from scattering amplitudes or worldline calculations. We extend these results to spinning black-hole probes up to and including second order in the probe spin and any order in the Post- Minkowskian expansion, for probe spins aligned with the Kerr spin. When truncating to third Post-Minkowskian order, our results agree with those obtained by amplitude and worldline methods., Comment: 18 pages, 3 tables

The post-Minkowskian expansion of Einstein's general theory of relativity has received much attention in recent years due to the possibility of harnessing the computational power of modern amplitude calculations in such a classical context. In this brief review, we focus on the post-Minkowskian expansion as applied to the two-body problem in general relativity without spin, and we describe how relativistic quantum field theory can be used to greatly simplify analytical calculations based on the Einstein-Hilbert action. Subtleties related to the extraction of classical physics from such quantum mechanical calculations highlight the care which must be taken when both positive and negative powers of Planck's constant are at play. In the process of obtaining classical results in both Einstein gravity and supergravity, one learns new aspects of quantum field theory that are obscured when using units in which Planck's constant is set to unity. The scattering amplitude approach provides a self-contained framework for deriving the two-body scattering valid in all regimes of energy. There is hope that the full impact of amplitude computations in this field may significantly alter the way in which gravitational wave predictions will advance in the coming years., Comment: 35 pages, see also the overview article. v2: minor corrections, published version

This is an introduction to, and invitation to read, a series of review articles on scattering amplitudes in gauge theory, gravity, and superstring theory. Our aim is to provide an overview of the field, from basic aspects to a selection of current (2022) research and developments., Comment: 15 pages, overview article. v3: journal version

The Effective One-Body formalism of the gravitational two-body problem in general relativity is reconsidered in the light of recent scattering amplitude calculations. Based on the kinematic relationship between momenta and the effective potential, we consider an energy-dependent effective metric describing the scattering in terms of an Effective One-Body problem for the reduced mass. The identification of the effective metric simplifies considerably in isotropic coordinates when combined with a redefined angular momentum map. While the effective energy-dependent metric as expected is not unique, solutions can be chosen perturbatively in the Post-Minkowskian expansion without the need to introduce non-metric corrections. By a canonical transformation, our condition maps to the one based on the standard angular momentum map. Expanding our metric around the Schwarzschild solution we recover the solution based on additional non-metric contributions., Comment: 10 pages. v3: stylistic corrections, version matching the published version in PRD

An exponential representation of the S-matrix provides a natural framework for understanding the semi-classical limit of scattering amplitudes. While sharing some similarities with the eikonal formalism it differs from it in details. Computationally, rules are simple because pieces that must be subtracted are given by combinations of unitarity cuts. Analyzing classical gravitational scattering to third Post-Minkowskian order in both maximal supergravity and Einstein gravity we find agreement with other approaches, including the contributions from radiation reaction terms. The kinematical relation for the two-body problem in isotropic coordinates follows immediately from this procedure, again with the inclusion of radiation reaction pieces up to third Post-Minkowskian order., Comment: 26 pages. v2: minor corrections. Version to appear in JHEP

We compute the scattering amplitude for classical black-hole scattering to third order in the Post-Minkowskian expansion, keeping all terms needed to derive the scattering angle to that order from the eikonal formalism. Our results confirm a conjectured relation between the real and imaginary parts of the amplitude by Di Vecchia, Heissenberg, Russo, and Veneziano, and are in agreement with a recent computation by Damour based on radiation reaction in general relativity., Comment: 33 pages. Several figures. v3 : affiliations and acknowledgements update, version to published in JHEP

We describe an efficient method for extracting the parts of $D$-dimensional loop integrals that are needed to derive observables in classical general relativity from scattering amplitudes. Our approach simplifies the soft-region method of integration by judiciously combining terms before the final integrations. We demonstrate the method by computing the required integrals for black-hole scattering to the second Post-Minkowskian order in Einstein gravity coupled to scalars. We also confirm recent results at the third Post-Minkowskian order regarding universality and high-energy behavior of gravitational interactions in maximal supergravity., Comment: 42 pages. v3: version to appear in PRD

We extract the long-range gravitational potential between two scalar particles with arbitrary masses from the two-to-two elastic scattering amplitude at 2nd Post-Minkowskian order in arbitrary dimensions. In contrast to the four-dimensional case, in higher dimensions the classical potential receives contributions from box topologies. Moreover, the kinematical relation between momentum and position on the classical trajectory contains a new term which is quadratic in the tree-level amplitude. A precise interplay between this new relation and the formula for the scattering angle ensures that the latter is still linear in the classical part of the scattering amplitude, to this order, matching an earlier calculation in the eikonal approach. We point out that both the eikonal exponentiation and the reality of the potential to 2nd post-Minkowskian order can be seen as a consequence of unitarity. We finally present closed-form expressions for the scattering angle given by leading-order gravitational potentials for dimensions ranging from four to ten., Comment: 51 pages, 1 figure, version to appear in JHEP

Using the implicit function theorem we demonstrate that solutions to the classical part of the relativistic Lippmann-Schwinger equation are in one-to-one correspondence with those of the energy equation of a relativistic two-body system. A corollary is that the scattering angle can be computed from the amplitude itself, without having to introduce a potential. All results are universal and provide for the case of general relativity a very simple formula for the scattering angle in terms of the classical part of the amplitude, to any order in the post-Minkowskian expansion., Comment: 24 pages, minor corrections, published version to appear in JHEP

We formulate an effective field theory describing large mass scalars and fermions minimally coupled to gravity. The operators of this effective field theory are organized in powers of the transfer momentum divided by the mass of the matter field, an expansion which lends itself to the efficient extraction of classical contributions from loop amplitudes in both the post-Newtonian and post-Minkowskian regimes. We use this effective field theory to calculate the classical and leading quantum gravitational scattering amplitude of two heavy spin-1/2 particles at the second post-Minkowskian order., Comment: 27 pages, 2 figures, corrected typo in electromagnetic spin-orbit amplitude

Using the CHY-formalism and its extension to a double cover we provide covariant expressions for tree-level amplitudes with two massive scalar legs and an arbitrary number of gravitons in D dimensions. Using unitarity methods, such amplitudes are needed inputs for the computation of post-Newtonian and post-Minkowskian expansions in classical general relativity., Comment: 25 pages

We describe the computation of post-Minkowskian Hamiltonians in General Relativity from scattering amplitudes. Using a relativistic Lippmann-Schwinger equation, we relate perturbative amplitudes of massive scalars coupled to gravity to the post-Minkowskian Hamiltonians of classical General Relativity to any order in Newton's constant. We illustrate this by deriving an Hamiltonian for binary black holes without spin up to 2nd order in the post-Minkowskian expansion and demonstrate explicitly the equivalence with the recently proposed method based on an effective field theory matching., Comment: 17 pages. v2: minor corrections version to appear in Physical Review D

A double-cover extension of the scattering equation formalism of Cachazo, He and Yuan (CHY) leads us to conjecture covariant factorization formulas of n-particle scattering amplitudes in Yang-Mills theories. Evidence is given that these factorization relations are related to Berends-Giele recursions through repeated use of partial fraction identities involving linearized propagators., Comment: 7 pages, 3 figures, version to appear in PRD

We outline the program to apply modern quantum field theory methods to calculate observables in classical general relativity through a truncation to classical terms of the multi-graviton two-body on-shell scattering amplitudes between massive fields. Since only long-distance interactions corresponding to non-analytic pieces need to be included, unitarity cuts provide substantial simplifications for both post-Newtonian and post-Minkowskian expansions. We illustrate this quantum field theoretic approach to classical general relativity by computing the interaction potentials to second order in the post-Newtonian expansion, as well as the scattering functions for two massive objects to second order in the post-Minkowskian expansion. We also derive an all-order exact result for gravitational light-by-light scattering., Comment: v2: 9 pages. Version to be published, minor corrections, references updated, and a new appendix on the eikonal method (a supplemental material at PRL)

We present some of the latest results from our numerical investigations of N=4 supersymmetric Yang--Mills theory formulated on a space-time lattice. Based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, we recently developed an improved lattice action that is now being employed in large-scale calculations. Here we update our studies of the static potential using this new action, also applying tree-level lattice perturbation theory to improve the analysis of the potential itself. Considering relatively weak couplings, we obtain results for the Coulomb coefficient that are consistent with continuum perturbation theory., Comment: Contribution to the proceedings of Lattice 2016, July 24--30, Southampton, UK

We show that all tree-level amplitudes in $\varphi^p$ scalar field theory can be represented as the $\alpha'\to0$ limit of an $SL(2,R)$-invariant, string-theory-like dual model integral. These dual models are constructed according to constraints that admit families of solutions. We derive these dual models, and give closed formulae for all tree-level amplitudes of any $\varphi^p$ scalar field theory., Comment: 15 pages, 0 figures

We prove that the scattering equation formalism for Yang-Mills amplitudes can be used to make manifest the theory's color-kinematics duality. This is achieved through a concrete reduction algorithm which renders this duality manifest term-by-term. The reduction follows from the recently derived set of identities for amplitudes expressed in the scattering equation formalism that are analogous to monodromy relations in string theory. A byproduct of our algorithm is a generalization of the identities among gravity and Yang-Mills amplitudes., Comment: 20 pages, 20 figures

Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space---fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Mobius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is a systematic procedure to obtain analytic, covariant forms of Yang-Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities., Comment: 29 pages, 43 figures; also included is a Mathematica notebook with explicit formulae. v2: citations added, and several (important) typos fixed

Electroweak baryogenesis is a simple and attractive candidate mechanism for generating the observed baryon asymmetry in the Universe. Its viability is sometimes investigated in terms of an effective field theory of the Standard Model involving higher dimension operators. We investigate the validity of such an effective field theory approach to the problem of identifying electroweak phase transitions strong enough for electroweak baryogenesis to be successful. We identify and discuss some pitfalls of this approach due to the modest hierarchy between mass scales of heavy degrees or freedom and the Higgs, and the possibility of dimensionful couplings violating the decoupling between light and heavy degrees of freedom., Comment: 18 pages + App. 17 figures. v2, References added

We propose a new framework to represent the perturbative S-matrix which is well-defined for all quantum field theories of massless particles, constructed from tree-level amplitudes and integrable term-by-term. This representation is derived from the Feynman expansion through a series of partial fraction identities, discarding terms that vanish upon integration. Loop integrands are expressed in terms of "Q-cuts" that involve both off-shell and on-shell loop-momenta, defined with a precise contour prescription that can be evaluated by ordinary methods. This framework implies recent results found in the scattering equation formalism at one-loop, and it has a natural extension to all orders---even non-planar theories without well-defined forward limits or good ultraviolet behavior., Comment: 4+1 pages, 4 figures

We formulate new integration rules for one-loop scattering equations analogous to those at tree-level, and test them in a number of non-trivial cases for amplitudes in scalar $\phi^3$-theory. This formalism greatly facilitates the evaluation of amplitudes in the CHY representation at one-loop order, without the need to explicitly sum over the solutions to the loop-level scattering equations., Comment: 22 pages, 17 figures

We show a direct matching between individual Feynman diagrams and integration measures in the scattering equation formalism of Cachazo, He and Yuan. The connection is most easily explained in terms of triangular graphs associated with planar Feynman diagrams in $\phi^3$-theory. We also discuss the generalization to general scalar field theories with $\phi^p$ interactions, corresponding to polygonal graphs involving vertices of order $p$. Finally, we describe how the same graph-theoretic language can be used to provide the precise link between individual Feynman diagrams and string theory integrands., Comment: 18 pages, 57 figures

As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any M\"obius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory., Comment: 30 pages, 29 figures

We report recent results and developments from our ongoing lattice studies of $\mathcal N = 4$ supersymmetric Yang--Mills theory. These include a proof that only a single fine-tuning needs to be performed, so long as the moduli space is not lifted by nonperturbative effects. We extend our investigations of supersymmetry restoration in the continuum limit by initiating Monte Carlo renormalization group studies. We present additional numerical evidence that the lattice theory does not suffer from a sign problem. Finally we study the static potential, which we find to be Coulombic at both weak and strong coupling. We compare the static potential Coulomb coefficients to perturbation theory, including initial results for N=3 colors in addition to N=2., Comment: 19-page combined contribution to the proceedings of Lattice 2014, for talks by SC, JG & DS. v2: Eq. 6.3 corrected, reference added

Maximally supersymmetric Yang--Mills theory in four dimensions can be formulated on a space-time lattice while exactly preserving a single supersymmetry. Here we explore in detail this lattice theory, paying particular attention to its strongly coupled regime. Targeting a theory with gauge group SU(N), the lattice formulation is naturally described in terms of gauge group U(N). Although the U(1) degrees of freedom decouple in the continuum limit we show that these degrees of freedom lead to unwanted lattice artifacts at strong coupling. We demonstrate that these lattice artifacts can be removed, leaving behind a lattice formulation based on the SU(N) gauge group with the expected apparently conformal behavior at both weak and strong coupling.

Scattering equations for tree-level amplitudes are viewed in the context of string theory. As a result of the comparison we are led to define a new dual model which coincides with string theory in both the small and large $\alpha'$ limit, and whose solution is found algebraically on the surface of solutions to the scattering equations. Because it has support only on the scattering equations, it can be solved exactly, yielding a simple resummed model for $\alpha'$-corrections to all orders. We use the same idea to generalize scattering equations to amplitudes with fermions and any mixture of scalars, gluons and fermions. In all cases checked we find exact agreement with known results., Comment: v2: 18 pp, 1 figure, added clarifications and comments. Version to be published in PRD

We demonstrate the power of constraining theories of new physics by insisting that they lead to electroweak baryogenesis, while agreeing with current data from the Large Hadron Collider. The general approach is illustrated with a singlet scalar extension of the Standard Model. Stringent bounds can already be obtained, which reduce the viable parameter space to a small island., Comment: 4 pages, 2 figures. References added, figures updated. Version to appear in PRL

Chiral perturbation theory for eigenvalue distributions, and equivalently random matrix theory, has recently been extended to include lattice effects for Wilson fermions. We test the predictions by comparison to eigenvalue distributions of the Hermitian Wilson-Dirac operator from pure gauge (quenched) ensembles. We show that the lattice effects are diminished when using clover improvement for the Dirac operator. We demonstrate that the leading Wilson low-energy constants associated with Wilson (clover) fermions can be determined using spectral information of the respective Dirac operator at finite volume., Comment: Presented at "Xth Quark Confinement and the Hadron Spectrum," October 2012, Garching, Germany. To appear as PoS (Confinement X) 077

We make a first study of the phase diagram of four-dimensional N=4 super Yang-Mills theory regulated on a space-time lattice. The lattice formulation we employ is both gauge invariant and retains at all lattice spacings one exactly preserved supersymmetry charge. Our numerical results are consistent with the existence of a single deconfined phase at all observed values of the bare coupling., Comment: 29 pages, 11 figures. References added, minor edits to text

We show how the leading physical and Wilson low-energy constants associated with Wilson fermions in lattice gauge theory can be determined individually by using spectral information of the Wilson Dirac operator with fixed index at finite volume. The methods are demonstrated in simulations with leading-order improved Wilson fermions. In addition to the expected suppression of the leading term in Wilson chiral perturbation theory we observe a substantial reduction also of the higher-order Wilson low-energy constants., Comment: 8 pages, 6 figures, references added, version to appear in Phys. Rev. D

We present the complete map of any pair of super Yang-Mills theories to supergravity theories as dictated by the KLT relations in four dimensions. Symmetries and the full set of associated vanishing identities are derived. A graphical method is introduced which simplifies counting of states, and helps in identifying the relevant set of symmetries., Comment: 41 pages, 16 figures, published version, typos corrected, references added

We discuss opportunities that may arise from subjecting high-multiplicity events in relativistic heavy ion collisions to an analysis similar to the one used in cosmology for the study of fluctuations of the Cosmic Microwave Background (CMB). To this end, we discuss examples of how pertinent features of heavy ion collisions including global characteristics, signatures of collective flow and event-wise fluctuations are visually represented in a Mollweide projection commonly used in CMB analysis, and how they are statistically analyzed in an expansion over spherical harmonic functions. If applied to the characterization of purely azimuthal dependent phenomena such as collective flow, the expansion coefficients of spherical harmonics are seen to contain redundancies compared to the set of harmonic flow coefficients commonly used in heavy ion collisions. Our exploratory study indicates, however, that these redundancies may offer novel opportunities for a detailed characterization of those event-wise fluctuations that remain after subtraction of the dominant collective flow signatures. By construction, the proposed approach allows also for the characterization of more complex collective phenomena like higher-order flow and other sources of fluctuations, and it may be extended to the characterization of phenomena of non-collective origin such as jets., Comment: Matches version accepted for publication in Physical Review C. 13 pages, 9 figures

Tree-level amplitudes of gauge theories are expressed in a basis of auxiliary amplitudes with only cubic vertices. The vertices in this formalism are explicitly factorized in color and kinematics, clarifying the color-kinematics duality in gauge theory amplitudes. The basis is constructed making use of the KK and BCJ relations, thereby showing precisely how these relations underlie the color-kinematics duality. We express gravity amplitudes in terms of a related basis of color-dressed gauge theory amplitudes, with basis coefficients which are permutation symmetric., Comment: 17 pages, 1 figure. v2: published version, example added in appendix

The microscopic spectral density of the Hermitian Wilson-Dirac operator is computed numerically in quenched lattice QCD. We demonstrate that the results given for fixed index of the Wilson-Dirac operator can be matched by the predictions from Wilson chiral perturbation theory. We test successfully the finite volume and the mass scaling predicted by Wilson chiral perturbation theory at fixed lattice spacing., Comment: 10 pages, 11 figures, version to appear in PRD

We investigate the existence of relations for finite one-loop amplitudes in Yang-Mills theory. Using a diagrammatic formalism and a remarkable connection between tree and loop level, we deduce sequences of amplitude relations for any number of external legs., Comment: 24 pages, 6 figures, v2 typos corrected, reference added

Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries., Comment: Lectures given as mini-course at the XIV Mexican School on Particles and Fields 2010

We discuss a set of recently discovered quadratic relations between gauge theory amplitudes. Such relations give additional structural simplifications for amplitudes in QCD. Remarkably, their origin lie in an analogous set of relations that involve also gravitons. When certain gluon helicities are flipped we obtain relations that do not involve gravitons, but which refer only to QCD., Comment: Talk given at XIV Mexican School on Particles and Fields, Morelia, Nov. 2010

We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral Perturbation Theory and chiral Random Matrix Theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac operator as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac operator. It is shown that a chiral Random Matrix Theory for the Wilson Dirac operator reproduces the leading zero-momentum terms of Wilson chiral Perturbation Theory. All results are obtained for fixed index of the Wilson Dirac operator. The low-energy constants of Wilson chiral Perturbation theory are shown to be constrained by the Hermiticity properties of the Wilson Dirac operator., Comment: 48 pages, 8 figures,v2 minor corrections same version as published in PRD

The QCD partition function for the Wilson Dirac operator, $D_W$, at nonzero lattice spacing $a$ can be expressed in terms of a chiral Lagrangian as a systematic expansion in the quark mass, the momentum and $a^2$. Starting from this chiral Lagrangian we obtain an analytical expression for the spectral density of $\gamma_5 (D_W+m)$ in the microscopic domain. It is shown that the $\gamma_5$-Hermiticity of the Dirac operator necessarily leads to a coefficient of the $a^2$ term that is consistent with the existence of an Aoki phase. The transition to the Aoki phase is explained, and the interplay of the index of $D_W$ and nonzero $a$ is discussed. We formulate a random matrix theory for the Wilson Dirac operator with index $\nu$ (which, in the continuum limit, becomes equal to the topological charge of gauge field configurations). It is shown by an explicit calculation that this random matrix theory reproduces the $a^2$-dependence of the chiral Lagrangian in the microscopic domain, and that the sign of the $a^2$-term is directly related to the $\gamma_5$-Hermiticity of $D_W$., Comment: 7 pages, 4 figures. Talk presented at the XXVIII International Symposium on Lattice Field Theory, Lattice2010, Villasimius, Italy, June 2010

Effects of dynamical quarks on the microscopic spectrum of the Wilson Dirac operator are analyzed by means of effective field theory. We consider the distributions of the real modes of the Wilson Dirac operator as well as the spectrum of the Hermitian Wilson Dirac operator, and work out the case of one flavor in all detail. In contrast to the quenched case, the theory has a mild sign problem that manifests itself by giving a spectral density that is not positive definite as the spectral gap closes., Comment: 7 pages 3 figures. Talk given at the XXVIII International Symposium on Lattice Field Theory (Lattice 2010), Villasimius, Italy, June 2010

We derive an explicit formula for factorizing an $n$-point closed string amplitude into open string amplitudes. Our results are phrased in terms of a momentum kernel which in the limit of infinite string tension reduces to the corresponding field theory kernel. The same momentum kernel encodes the monodromy relations which lead to the minimal basis of color-ordered amplitudes in Yang-Mills theory. There are interesting consequences of the momentum kernel pertaining to soft limits of amplitudes. We also comment on surprising links between gravity and certain combinations of kinematic and color factors in gauge theory., Comment: 19 pages, 1 figure

Using BCFW on-shell recursion techniques, we prove a sequence of explicit n-point Kawai-Lewellen-Tye relations between gravity and Yang-Mills amplitudes at tree level., Comment: 17 pages, no figures, JHEP

Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N=4 super Yang-Mills multiplet., Comment: 7 pages

Using only general features of the S-matrix and quantum field theory, we prove by induction the Kawai-Lewellen-Tye relations that link products of gauge theory amplitudes to gravity amplitudes at tree level. As a bonus of our analysis, we provide a novel and more symmetric form of these relations. We also establish an infinite tower of new identities between amplitudes in gauge theories., Comment: 4 pages, REVTeX, minor typos corrected and references added. Published version

We discuss monodromy relations between different color-ordered amplitudes in gauge theories. We show that Jacobi-like relations of Bern, Carrasco and Johansson can be introduced in a manner that is compatible with these monodromy relations. The Jacobi-like relations are not the most general set of equations that satisfy this criterion. Applications to supergravity amplitudes follow straightforwardly through the KLT-relations. We explicitly show how the tree-level relations give rise to non-trivial identities at loop level., Comment: 28 pages, 8 figures, JHEP3

We calculate the leading contribution to the spectral density of the Wilson Dirac operator using chiral perturbation theory where volume and lattice spacing corrections are given by universal scaling functions. We find analytical expressions for the spectral density on the scale of the average level spacing, and introduce a chiral Random Matrix Theory that reproduces these results. Our work opens up a novel approach to the infinite volume limit of lattice gauge theory at finite lattice spacing and new ways to extract coefficients of Wilson chiral perturbation theory., Comment: 4 pages, 3 figures, refs added, version to appear in Phys. Rev. Lett

Identities based on monodromy for integrations in string theory are used to derive relations between different color ordered tree-level amplitudes in both bosonic and supersymmetric string theory. These relations imply that the color ordered tree-level n-point gauge theory amplitudes can be expanded in a minimal basis of (n-3)! amplitudes. This result holds for any choice of polarizations of the external states and in any number of dimensions., Comment: v2: typos corrected, some rephrasing of the general discussion. Captions to figures added. Version to appear in PRL. 4 pages, 5 figures