scholarly journals Cosmological correlators, In–In formalism and double copy

2020 ◽  
Vol 35 (11) ◽  
pp. 2050076 ◽  
Author(s):  
A. R. Fazio
Keyword(s):  
Scattering Amplitudes ◽  
Scalar Curvature ◽  
Gravitational Waves ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Tree Level ◽  
Tensor Factor ◽  
Dimensional Minkowski Space ◽  
Primordial Gravitational Waves ◽  
Double Copy

We are investigating if the double copy structure as product of scattering amplitudes of gauge theories applies to cosmological correlators computed, in a class of theories for inflation, by the operatorial version of the In–In formalism of Schwinger–Keldysh. We consider tree-level momentum–space correlators involving primordial gravitational waves with different polarizations and the scalar curvature fluctuations on a three-dimensional fixed spatial slice. The correlators are sum of terms factorized in a time-dependent scalar factor, which takes into account the curved background where energy is not conserved, and in a so-called tensor factor, constructed by polarization tensors. In the latter, we recognize scattering amplitudes in four-dimensional Minkowski space spanned by three points gravitational amplitudes related by double copy to those of gauge theories. Our study indicates that gravitational waves are double copy of gluons and the primordial scalar curvature is double copy of a scalar with Higgs-like interactions.

scholarly journals Scattering amplitudes and the double copy in topologically massive theories

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Nathan Moynihan
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitudes ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Landau Gauge ◽  
Massive Gravity ◽  
Gauge Bosons ◽  
Four Dimensions ◽  
Recent Developments ◽  
Double Copy

Abstract Using the principles of the modern scattering amplitudes programme, we develop a formalism for constructing the amplitudes of three-dimensional topologically massive gauge theories and gravity. Inspired by recent developments in four dimensions, we construct the three-dimensional equivalent of x-variables, first defined in [1], for conserved matter currents coupled to topologically massive gauge bosons or gravitons. Using these, we bootstrap various matter-coupled gauge-theory and gravitational scattering amplitudes, and conjecture that topologically massive gauge theory and topologically massive gravity are related by the double copy. To motivate this idea further, we show explicitly that the Landau gauge propagator on the gauge theory side double copies to the de Donder gauge propagator on the gravity side.

scholarly journals PROBING THE FROISSART BOUND FOR MODELS WITH CHARGED VECTOR FIELDS IN D=3

1994 ◽  
Vol 09 (18) ◽  
pp. 1695-1700 ◽  
Author(s):  
O.M. DEL CIMA
Keyword(s):  
Asymptotic Behavior ◽  
Scattering Amplitudes ◽  
Gauge Field ◽  
Vector Fields ◽  
Three Dimensional ◽  
Tree Level ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Maxwell Fields ◽  
Chern Simons

One discusses the tree-level unitarity and presents asymptotic behavior of scattering amplitudes for three-dimensional gauge-invariant models where complex Chern- Simons-Maxwell fields (with and without a Proca-like mass) are coupled to an Abelian gauge field.

scholarly journals Massive double copy in three spacetime dimensions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Mariana Carrillo González ◽  
Arshia Momeni ◽  
Justinas Rumbutis
Keyword(s):  
Scattering Amplitudes ◽  
Three Dimensional ◽  
Massive Gravity ◽  
Gauge Fields ◽  
Yang Mills ◽  
Double Copy ◽  
Topologically Massive Gravity

Abstract Recent explorations on how to construct a double copy of massive gauge fields have shown that, while any amplitude can be written in a form consistent with colour-kinematics duality, the double copy is generically unphysical. In this paper, we explore a new direction in which we can obtain a sensible double copy of massive gauge fields due to the special kinematics in three-dimensional spacetimes. To avoid the appearance of spurious poles at 5-points, we only require that the scattering amplitudes satisfy one BCJ relation. We show that the amplitudes of Topologically Massive Yang-Mills satisfy this relation and that their double copy at three, four, and five-points is Topologically Massive Gravity.

scholarly journals The L∞ structure of gauge theories with matter

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Humberto Gomez ◽  
Renann Lipinski Jusinskas ◽  
Cristhiam Lopez-Arcos ◽  
Alexander Quintero Vélez
Keyword(s):  
Perturbation Theory ◽  
Scattering Amplitudes ◽  
Quantum Chromodynamics ◽  
Minimal Model ◽  
Gauge Theories ◽  
Algebraic Approach ◽  
Field Theories ◽  
Tree Level ◽  
Scalar Quantum ◽  
Chern Simons

Abstract In this work we present an algebraic approach to the dynamics and perturbation theory at tree-level for gauge theories coupled to matter. The field theories we will consider are: Chern-Simons-Matter, Quantum Chromodynamics, and scalar Quantum Chromodynamics. Starting with the construction of the master action in the classical Batalin-Vilkovisky formalism, we will extract the L∞-algebra that allow us to recursively calculate the perturbiner expansion from its minimal model. The Maurer-Cartan action obtained in this procedure will then motivate a generating function for all the tree-level scattering amplitudes. There are two interesting outcomes of this construction: a generator for fully-flavoured amplitudes via a localisation on Dyck words; and closed expressions for fermion and scalar lines attached to n-gluons with arbitrary polarisations.

scholarly journals The single copy of the gravitational holonomy

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Rashid Alawadhi ◽  
David S. Berman ◽  
Chris D. White ◽  
Sam Wikeley
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitudes ◽  
Gauge Theories ◽  
Holonomy Group ◽  
Single Copy ◽  
Classical Solutions ◽  
Established Relationship ◽  
Double Copy

Abstract The double copy is a well-established relationship between gravity and gauge theories. It relates perturbative scattering amplitudes as well as classical solutions, and recently there has been mounting evidence that it also applies to non-perturbative information. In this paper, we consider the holonomy properties of manifolds in gravity and prescribe a single copy of gravitational holonomy that differs from the holonomy in gauge theory. We discuss specific cases and give examples where the single copy holonomy group is reduced. Our results may prove useful in extending the classical double copy. We also clarify previous misconceptions in the literature regarding gravitational Wilson lines and holonomy.

scholarly journals Non-Gaussianity of inflationary gravitational waves from the field equation

2019 ◽  
Vol 28 (02) ◽  
pp. 1950036 ◽  
Author(s):  
Aniket Agrawal
Keyword(s):  
Field Equation ◽  
Green’S Function ◽  
Gravitational Waves ◽  
Green's Function ◽  
Tree Level ◽  
Gauge Fields ◽  
Vacuum Fluctuations ◽  
Scale Invariant ◽  
Left Handed ◽  
Primordial Gravitational Waves

We demonstrate equivalence of the in–in formalism and Green’s function method for calculating the bispectrum of primordial gravitational waves generated by vacuum fluctuations of the metric. The tree-level bispectrum from the field equation, [Formula: see text], agrees with the results obtained previously using the in–in formalism exactly. Characterizing non-Gaussianity of the fluctuations using the ratio [Formula: see text] in the equilateral configuration, where [Formula: see text] is the power spectrum of scale-invariant gravitational waves, we show that it is much weaker than in models with spectator gauge fields. We also calculate the tree-level bispectrum of two right-handed and one left-handed gravitational wave using Green’s function, reproducing the results from in–in formalism, and show that it can be as large as the bispectrum of three right-handed gravitational waves.

scholarly journals Anyons and the double copy

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Daniel J Burger ◽  
William T. Emond ◽  
Nathan Moynihan
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitudes ◽  
Long Range ◽  
Topological Structure ◽  
Three Dimensions ◽  
Tree Level ◽  
Curved Spacetime ◽  
Range Tree ◽  
Aharonov Bohm ◽  
Double Copy

Abstract We examine the double copy structure of anyons in gauge theory and gravity. Using on-shell amplitude techniques, we construct little group covariant spinor-helicity variables describing massive particles with spin, which together with locality and unitarity enables us to derive the long-range tree-level scattering amplitudes involving anyons. We discover that classical gauge theory anyon solutions double copy to their gravitational counterparts in a non-trivial manner. Interestingly, we show that the massless double copy captures the topological structure of curved spacetime in three dimensions by introducing a non-trivial mixing of the topological graviton and the dilaton. Finally, we show that the celebrated Aharonov-Bohm phase can be derived directly from the constructed on-shell amplitude, and that it too enjoys a simple double copy to its gravitational counterpart.

scholarly journals Extracting Einstein from the loop-level double-copy

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
John Joseph M. Carrasco ◽  
Ingrid A. Vazquez-Holm
Keyword(s):  
Classical Limit ◽  
Gauge Theories ◽  
Gravitational Theory ◽  
Tree Level ◽  
The Novel ◽  
Massive Scalar ◽  
Massive Black Hole ◽  
Loop Level ◽  
Double Copy ◽  
Systematic Framework

Abstract The naive double-copy of (multi) loop amplitudes involving massive matter coupled to gauge theories will generically produce amplitudes in a gravitational theory that contains additional contributions from propagating antisymmetric tensor and dilaton states even at tree-level. We present a graph-based approach that combines the method of maximal cuts with double-copy construction to offer a systematic framework to isolate the pure Einstein-Hilbert gravitational contributions through loop level. Indeed this allows for a bootstrap of pure-gravitational results from the double-copy of massive scalar-QCD. We apply this to construct the novel result of the D-dimensional one-loop five-point QFT integrand relevant in the classical limit to generating observables associated with the radiative effects of massive black-hole scattering via pure Einstein-Hilbert gravity.

scholarly journals Wilson loop algebras and quantum K-theory for Grassmannians

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hans Jockers ◽  
Peter Mayr ◽  
Urmi Ninad ◽  
Alexander Tabler
Keyword(s):  
Wilson Loop ◽  
Gauge Theories ◽  
Wilson Line ◽  
Quantum Cohomology ◽  
Three Dimensional ◽  
Loop Algebra ◽  
Loop Algebras ◽  
Verlinde Algebra ◽  
K Theory ◽  
Chern Simons

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

scholarly journals On polytopes and generalizations of the KLT relations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Nikhil Kalyanapuram
Keyword(s):  
Scattering Amplitudes ◽  
Large Class ◽  
Moduli Space ◽  
Differential Forms ◽  
Natural Generalization ◽  
Intersection Theory ◽  
Hyperplane Arrangements ◽  
Number Of Solutions ◽  
Scalar Theories ◽  
Double Copy

Abstract We combine the technology of the theory of polytopes and twisted intersection theory to derive a large class of double copy relations that generalize the classical relations due to Kawai, Lewellen and Tye (KLT). To do this, we first study a generalization of the scattering equations of Cachazo, He and Yuan. While the scattering equations were defined on ℳ0, n — the moduli space of marked Riemann spheres — the new scattering equations are defined on polytopes known as accordiohedra, realized as hyperplane arrangements. These polytopes encode as patterns of intersection the scattering amplitudes of generic scalar theories. The twisted period relations of such intersection numbers provide a vast generalization of the KLT relations. Differential forms dual to the bounded chambers of the hyperplane arrangements furnish a natural generalization of the Bern-Carrasco-Johansson (BCJ) basis, the number of which can be determined by counting the number of solutions of the generalized scattering equations. In this work the focus is on a generalization of the BCJ expansion to generic scalar theories, although we use the labels KLT and BCJ interchangeably.

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