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 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 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 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 Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

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.

scholarly journals Three-dimensional 𝒩 = 2 supersymmetric gauge theories and partition functions on Seifert manifolds: A review

2019 ◽  
Vol 34 (23) ◽  
pp. 1930011 ◽  
Author(s):  
Cyril Closset ◽  
Heeyeon Kim
Keyword(s):  
Correlation Functions ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Partition Functions ◽  
Exact Results ◽  
Strongly Coupled ◽  
Seifert Manifolds ◽  
Recent Developments ◽  
Supersymmetric Gauge ◽  
Chern Simons

We give a pedagogical introduction to the study of supersymmetric partition functions of 3D [Formula: see text] supersymmetric Chern–Simons-matter theories (with an [Formula: see text]-symmetry) on half-BPS closed three-manifolds — including [Formula: see text], [Formula: see text], and any Seifert three-manifold. Three-dimensional gauge theories can flow to nontrivial fixed points in the infrared. In the presence of 3D [Formula: see text] supersymmetry, many exact results are known about the strongly-coupled infrared, due in good part to powerful localization techniques. We review some of these techniques and emphasize some more recent developments, which provide a simple and comprehensive formalism for the exact computation of half-BPS observables on closed three-manifolds (partition functions and correlation functions of line operators). Along the way, we also review simple examples of 3D infrared dualities. The computation of supersymmetric partition functions provides exceedingly precise tests of these dualities.

scholarly journals The World as Quarks, Leptons and Bosons

1976 ◽  
Vol 29 (6) ◽  
pp. 347 ◽  
Author(s):  
M Gell-Mann
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Strong Interactions ◽  
Gauge Bosons ◽  
Yang Mills ◽  
Electromagnetic Interactions ◽  
The World

A descriptive review is given of gauge theories of weak, electromagnetic and strong interactions. The strong interactions are interpreted in terms of an unbroken Yang-Mills gauge theory based on SU(3) colour symmetry of quarks and gluons. The confinement mechanism of quarks, gluons and other nonsinglets is discussed. The unification of the weak and electromagnetic interactions through a broken Yang-Mills gauge theory is described. In total the basic constituents are then the quarks, leptons and gauge bosons.

scholarly journals FOUR LECTURES ON THE GAUGE/GRAVITY CORRESPONDENCE

2003 ◽  
Vol 18 (31) ◽  
pp. 5647-5711 ◽  
Author(s):  
MATTEO BERTOLINI
Keyword(s):  
Gauge Theory ◽  
Riemann Surfaces ◽  
Gauge Theories ◽  
Open Problems ◽  
Four Dimensions ◽  
General Overview ◽  
Geometric Transitions ◽  
Supersymmetric Gauge ◽  
Gauge Gravity ◽  
M Theory

We review in a pedagogical manner some of the efforts aimed at extending the gauge/gravity correspondence to nonconformal supersymmetric gauge theories in four dimensions. After giving a general overview, we discuss in detail two specific examples: fractional D-branes on orbifolds and D-branes wrapped on supersymmetric cycles of Calabi–Yau spaces. We explore in particular which gauge theory information can be extracted from the corresponding supergravity solutions, and what the remaining open problems are. We also briefly explain the connection between these and other approaches, such as fractional branes on conifolds, branes suspended between branes, M5-branes on Riemann surfaces and M-theory on G2-holonomy manifolds, and discuss the role played by geometric transitions in all that.

scholarly journals Two Lectures on the Jones Polynomial and Khovanov Homology

2017 ◽  
Author(s):  
Edward Witten
Keyword(s):  
Gauge Theory ◽  
Three Dimensional ◽  
Jones Polynomial ◽  
Khovanov Homology ◽  
Theory Approach ◽  
Laurent Polynomials ◽  
Four Dimensions ◽  
Knot Invariants ◽  
Fifth Dimension ◽  
Instanton Number

In the first of these two lectures I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable q. The two main steps are to reinterpret three-dimensional Chern-Simons gauge theory in four dimensional terms and then to apply electric-magnetic duality. The variable q is associated to instanton number in the dual description in four dimensions. In the second lecture, I describe how Khovanov homology can emerge upon adding a fifth dimension.

scholarly journals Classical and quantum double copy of back-reaction

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Tim Adamo ◽  
Anton Ilderton
Keyword(s):  
Quantum Theory ◽  
Gauge Theory ◽  
Plane Wave ◽  
Tree Level ◽  
Back Reaction ◽  
Quantum Double ◽  
Four Dimensions ◽  
Helicity Formalism ◽  
Massive Spinor ◽  
Double Copy

Abstract We consider radiation emitted by colour-charged and massive particles crossing strong plane wave backgrounds in gauge theory and gravity. These backgrounds are treated exactly and non-perturbatively throughout. We compute the back-reaction on these fields from the radiation emitted by the probe particles: classically through background-coupled worldline theories, and at tree-level in the quantum theory through three-point amplitudes. Consistency of these two methods is established explicitly. We show that the gauge theory and gravity amplitudes are related by the double copy for amplitudes on plane wave backgrounds. Finally, we demonstrate that in four-dimensions these calculations can be carried out with a background-dressed version of the massive spinor-helicity formalism.

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