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 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 Classical solutions and their double copy in split signature

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ricardo Monteiro ◽  
Donal O’Connell ◽  
David Peinador Veiga ◽  
Matteo Sergola
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitudes ◽  
Coherent State ◽  
Building Block ◽  
Classical Solutions ◽  
Lorentzian Signature ◽  
Spacetime Metric ◽  
Set Up ◽  
Double Copy ◽  
Point Amplitude

Abstract The three-point amplitude is the key building block in the on-shell approach to scattering amplitudes. We show that the classical objects computed by massive three-point amplitudes in gauge theory and gravity are Newman-Penrose scalars in a split-signature spacetime, where three-point amplitudes can be defined for real kinematics. In fact, the quantum state set up by the particle is a coherent state fully determined by the three-point amplitude due to an eikonal-type exponentiation. Having identified this simplest classical solution from the perspective of scattering amplitudes, we explore the double copy of the Newman-Penrose scalars induced by the traditional double copy of amplitudes, and find that it coincides with the Weyl version of the classical double copy. We also exploit the Kerr-Schild version of the classical double copy to determine the exact spacetime metric in the gravitational case. Finally, we discuss the direct implication of these results for Lorentzian signature via analytic continuation.

Gravity as a double copy of gauge theory: from amplitudes to black holes

2015 ◽  
Vol 24 (09) ◽  
pp. 1542008 ◽  
Author(s):  
Ricardo Monteiro ◽  
Donal O'Connell ◽  
Chris D. White
Keyword(s):  
Black Holes ◽  
Gauge Theory ◽  
Algebraic Structure ◽  
Plane Waves ◽  
The Self ◽  
Classical Solutions ◽  
Color Structure ◽  
Double Copy ◽  
Insight Into

We discuss the relation between perturbative gauge theory and perturbative gravity, and look at how this relation extends to some exact classical solutions. First, we give an overview of the double copy prescription that takes gauge theory amplitudes into gravity amplitudes, which has been crucial to progress in perturbative studies of supergravity. Then, we review how the self-dual sectors provide an important insight into the relation between the theories. A key role is played by a kinematic algebraic structure mirroring the color structure. Finally, we review how these ideas extend to some exact classical solutions, namely black holes and plane waves.

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 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.

Perturbative gravity from gauge theory

2014 ◽  
Vol 29 (32) ◽  
pp. 1430036 ◽  
Author(s):  
Z. Bern
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitudes ◽  
Recent Calculation ◽  
Loop Level ◽  
Double Copy

Here, we describe a recently conjectured duality between color and kinematics for gauge-theory amplitudes. Whenever this duality is manifest, the integrands of loop-level gravity scattering amplitudes can be obtained from corresponding gauge-theory amplitudes via a double-copy relation. This duality has been used to enormously simplify a number of explicit multiloop supergravity calculations. The results of these computations is that supergravity theories have a surprisingly tame ultraviolet behavior, and in some cases may even be finite. As an example, we summarize a recent calculation showing that half-maximal [Formula: see text] supergravity in four spacetime dimensions is ultraviolet finite at three loops, contrary to previous expectations.

scholarly journals The Volume of the Quiver Vortex Moduli Space

2021 ◽  
Author(s):  
Kazutoshi Ohta ◽  
Norisuke Sakai
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Gauge Theories ◽  
Target Space ◽  
Contour Integral ◽  
Quiver Gauge Theory ◽  
Volume Formula ◽  
Volume Operator ◽  
Space Volume

Abstract We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of a suitable cohomological operator (volume operator) in a supersymmetric quiver gauge theory, where BPS equations of the vortices are embedded. In the supersymmetric gauge theory, the moduli space volume is exactly evaluated as a contour integral by using the localization. Graph theory is useful to construct the supersymmetric quiver gauge theory and to derive the volume formula. The contour integral formula of the volume (generalization of the Jeffrey-Kirwan residue formula) leads to the Bradlow bounds (upper bounds on the vorticity by the area of the Riemann surface divided by the intrinsic size of the vortex). We give some examples of various quiver gauge theories and discuss properties of the moduli space volume in these theories. Our formula are applied to the volume of the vortex moduli space in the gauged non-linear sigma model with CPN target space, which is obtained by a strong coupling limit of a parent quiver gauge theory. We also discuss a non-Abelian generalization of the quiver gauge theory and “Abelianization” of the volume formula.

scholarly journals The Kerr-Schild double copy in Lifshitz spacetime

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Gökhan Alkaç ◽  
Mehmet Kemal Gümüş ◽  
Mustafa Tek
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Charge Density ◽  
Localized Source ◽  
Curvature Term ◽  
Constant Charge Density ◽  
Arbitrary Dimensions ◽  
Double Copy ◽  
Theory Solution ◽  
Constant Charge

Abstract The Kerr-Schild double copy is a map between exact solutions of general relativity and Maxwell’s theory, where the nonlinear nature of general relativity is circumvented by considering solutions in the Kerr-Schild form. In this paper, we give a general formulation, where no simplifying assumption about the background metric is made, and show that the gauge theory source is affected by a curvature term that characterizes the deviation of the background spacetime from a constant curvature spacetime. We demonstrate this effect explicitly by studying gravitational solutions with non-zero cosmological constant. We show that, when the background is flat, the constant charge density filling all space in the gauge theory that has been observed in previous works is a consequence of this curvature term. As an example of a solution with a curved background, we study the Lifshitz black hole with two different matter couplings. The curvature of the background, i.e., the Lifshitz spacetime, again yields a constant charge density; however, unlike the previous examples, it is canceled by the contribution from the matter fields. For one of the matter couplings, there remains no additional non-localized source term, providing an example for a non-vacuum gravity solution corresponding to a vacuum gauge theory solution in arbitrary dimensions.

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.

scholarly journals Two-loop rational terms in Yang-Mills theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jean-Nicolas Lang ◽  
Stefano Pozzorini ◽  
Hantian Zhang ◽  
Max F. Zoller
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Theories ◽  
A Posteriori ◽  
Four Dimensions ◽  
Yang Mills ◽  
General Properties ◽  
Finite Set ◽  
Numerical Tools ◽  
Loop Amplitudes

Abstract Scattering amplitudes in D dimensions involve particular terms that originate from the interplay of UV poles with the (D − 4)-dimensional parts of loop numerators. Such contributions can be controlled through a finite set of process-independent rational counterterms, which make it possible to compute loop amplitudes with numerical tools that construct the loop numerators in four dimensions. Building on a recent study [1] of the general properties of two-loop rational counterterms, in this paper we investigate their dependence on the choice of renormalisation scheme. We identify a nontrivial form of scheme dependence, which originates from the interplay of mass and field renormalisation with the (D−4)-dimensional parts of loop numerators, and we show that it can be controlled through a new kind of one-loop counterterms. This guarantees that the two-loop rational counterterms for a given renormalisable theory can be derived once and for all in terms of generic renormalisation constants, which can be adapted a posteriori to any scheme. Using this approach, we present the first calculation of the full set of two-loop rational counterterms in Yang-Mills theories. The results are applicable to SU(N) and U(1) gauge theories coupled to nf fermions with arbitrary masses.

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