Celestial double copy from the worldsheet
TL;DR: In this article, the ambitwistor string is used to compute tree-level celestial amplitudes for bi-adjoint scalars, Yang-Mills and gravity to all multiplicities.
Abstract: Using the ambitwistor string, we compute tree-level celestial amplitudes for biadjoint scalars, Yang-Mills and gravity to all multiplicities. They are presented in compact CHY-like formulas with operator-valued scattering equations and numerators acting on a generalized hypergeometric function. With these we extend the celestial double copy to tree-level amplitudes with arbitrary number of external states. We also show how color-kinematics duality is implemented in celestial amplitudes and its interpretation in terms of a generalized twisted cohomology theory.
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TL;DR: In this article, the authors construct two towers of 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights, which generate the symmetries associated to an infinite tower of conformally soft theorems.
Abstract: All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of conformally soft theorems. The current algebra commutators are explicitly derived from the poles in the OPE coefficients, and found to comprise a rich closed subalgebra of the complete symmetry algebra.
144 citations
TL;DR: In this article, it was shown that known UV and IR properties of quantum gravity translate into powerful constraints on the analytic structure of celestial amplitudes, and exclusive amplitudes are shown to simply factorize into conformally hard and conformally soft factors.
Abstract: Celestial amplitudes represent 4D scattering of particles in boost, rather than the usual energy-momentum, eigenstates and hence are sensitive to both UV and IR physics. We show that known UV and IR properties of quantum gravity translate into powerful constraints on the analytic structure of celestial amplitudes. For example the soft UV behavior of quantum gravity is shown to imply that the exact four-particle scattering amplitude is meromorphic in the complex boost weight plane with poles confined to even integers on the negative real axis. Would-be poles on the positive real axis from UV asymptotics are shown to be erased by a flat space analog of the AdS resolution of the bulk point singularity. The residues of the poles on the negative axis are identified with operator coefficients in the IR effective action. Far along the real positive axis, the scattering is argued to grow exponentially according to the black hole area law. Exclusive amplitudes are shown to simply factorize into conformally hard and conformally soft factors. The soft factor contains all IR divergences and is given by a celestial current algebra correlator of Goldstone bosons from spontaneously broken asymptotic symmetries. The hard factor describes the scattering of hard particles together with the boost-eigenstate clouds of soft photons or gravitons required by asymptotic symmetries. These provide an IR safe $\mathcal{S}$-matrix for the scattering of hard particles.
70 citations
TL;DR: The Weyl double copy as discussed by the authors is a procedure for relating exact solutions in bi-joint scalar, gauge and gravity theories, and relates fields in spacetime directly, but its exact form and scope have until recently remained mysterious.
Abstract: The Weyl double copy is a procedure for relating exact solutions in biadjoint scalar, gauge and gravity theories, and relates fields in spacetime directly. Where this procedure comes from, and how general it is, have until recently remained mysterious. In this paper, we show how the current form and scope of the Weyl double copy can be derived from a certain procedure in twistor space. The new formalism shows that the Weyl double copy is more general than previously thought, applying in particular to gravity solutions with arbitrary Petrov types. We comment on how to obtain anti-self-dual as well as self-dual fields, and clarify some conceptual issues in the twistor approach.
70 citations
TL;DR: In this article, it was shown that known UV and IR properties of quantum gravity translate into powerful constraints on the analytic structure of celestial amplitudes, and exclusive amplitudes are shown to simply factorize into conformally hard and conformally soft factors.
Abstract: Celestial amplitudes represent 4D scattering of particles in boost, rather than the usual energy-momentum, eigenstates and hence are sensitive to both UV and IR physics. We show that known UV and IR properties of quantum gravity translate into powerful constraints on the analytic structure of celestial amplitudes. For example the soft UV behavior of quantum gravity is shown to imply that the exact four-particle scattering amplitude is meromorphic in the complex boost weight plane with poles confined to even integers on the negative real axis. Would-be poles on the positive real axis from UV asymptotics are shown to be erased by a flat space analog of the AdS resolution of the bulk point singularity. The residues of the poles on the negative axis are identified with operator coefficients in the IR effective action. Far along the real positive axis, the scattering is argued to grow exponentially according to the black hole area law. Exclusive amplitudes are shown to simply factorize into conformally hard and conformally soft factors. The soft factor contains all IR divergences and is given by a celestial current algebra correlator of Goldstone bosons from spontaneously broken asymptotic symmetries. The hard factor describes the scattering of hard particles together with the boost-eigenstate clouds of soft photons or gravitons required by asymptotic symmetries. These provide an IR safe $$ \mathcal{S} $$
-matrix for the scattering of hard particles.
46 citations
Book•
01 Jan 1997
TL;DR: The story of the configuration space X (2,4) of n Points on the Projective Line: The Configuration Space X ( 2,5), Hypergeometric Functions of Type (3,6), Modular Interpretation of the Configuration Space x (3.6) as mentioned in this paper.
Abstract: Part 1: The Story of the Configuration Space X (2,4) of Four Points on the Projective Line: Configuration Spaces - The Simplest Case Elliptic Curves Modular Interpretations of X (2,4) Hypergeometric Integrals and Loaded Cycles. Part 2: The Story of the Configuration Space X (2,n) of n Points on the Projective Line: The Configuration Space X (2,5) Modular Interpretation of the Configuration Space X (2,n) The Configuration Space X (3,6) Hypergeometric Functions of Type (3,6) Modular Interpretation of the Configuration Space X (3,6)
38 citations
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TL;DR: In this paper, Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves, which is a consequence of an equivalence between the perturbative expansion of = 4 super Yang-Mills theory and the D-instanton expansion of a certain string theory.
Abstract: Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves. This in turn is apparently a consequence of an equivalence between the perturbative expansion of = 4 super Yang-Mills theory and the D-instanton expansion of a certain string theory, namely the topological B model whose target space is the Calabi-Yau supermanifold
1,626 citations
TL;DR: In this paper, an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories is presented, which is an analog of the Jacobi identity for color factors.
Abstract: 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 Kawai-Lewellen-Tye (KLT) relations between gauge and gravity tree amplitudes. This insight leads to similar but novel relations. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.
1,434 citations
"Celestial double copy from the worl..." refers background or methods in this paper
...While in the ambitwistor string the double copy amounts to a substitution rule, using traditional methods it relies on kinematical numerators satisfying the so-called color-kinematics duality [32], that is, they obey relations analogous to Jacobi identities among color factors....
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...These kind of numerators are called color-kinematical dual numerators [32]....
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TL;DR: It is 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.
Abstract: 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 nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.
1,046 citations
"Celestial double copy from the worl..." refers methods in this paper
...The double copy is a procedure to obtain gravitational amplitudes from a “square” of YangMills amplitudes [31]....
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...3 Color-kinematics duality and double copy The original double copy [31] is a prescription to obtain gravitational amplitudes from suitable squares of Yang-Mills amplitudes....
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TL;DR: A compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimensions is presented and Gauge invariance is completely manifest as it follows from a simple property of the Pfaffian.
Abstract: A new formula for the scattering of massless particles may simplify predictions and analyses of LHC experiments and shed new light on quantum gravity theories.
828 citations
"Celestial double copy from the worl..." refers background or methods in this paper
...2 CHY formulas The CHY formulas present the D-dimensional, tree-level massless S-matrix of several quantum field theories [27, 28, 44] as an integral formula....
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...This is a worldsheet theory from which the CHY formulas [27, 28] can be obtained as correlation functions of vertex operators in a chiral CFT....
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TL;DR: In this paper, a natural formulation for a massless colored cubic scalar theory is presented, which is an integral over the space of n marked points on a sphere and has as integrand two factors: the first is a combination of Parke-Taylor-like terms dressed with U(N ) color structures while the second is a Pfaffian.
Abstract: In a recent note we presented a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimension. In this paper we show that a natural formulation also exists for a massless colored cubic scalar theory. In Yang-Mills, the formula is an integral over the space of n marked points on a sphere and has as integrand two factors. The first factor is a combination of Parke-Taylor-like terms dressed with U(N ) color structures while the second is a Pfaffian. The S-matrix of a U(N ) × U(N ) cubic scalar theory is obtained by simply replacing the Pfaffian with a U(N ) version of the previous U(N ) factor. Given that gravity amplitudes are obtained by replacing the U(N ) factor in Yang-Mills by a second Pfaffian, we are led to a natural color-kinematics correspondence. An expansion of the integrand of the scalar theory leads to sums over trivalent graphs and are directly related to the KLT matrix. Combining this and the Yang-Mills formula we find a connection to the BCJ color-kinematics duality as well as a new proof of the BCJ doubling property that gives rise to gravity amplitudes. We end by considering a special kinematic point where the partial amplitude simply counts the number of color-ordered planar trivalent trees, which equals a Catalan number. The scattering equations simplify dramatically and are equivalent to a special Y-system with solutions related to roots of Chebyshev polynomials. The sum of the integrand over the solutions gives rise to a representation of Catalan numbers in terms of eigenvectors and eigenvalues of the adjacency matrix of an A-type Dynkin diagram.
611 citations