Gauge invariant double copy of Yang-Mills theory: the quartic theory

Bonezzi, Roberto; Chiaffrino, Christoph; Felipe, Diaz-Jaramillo,; Hohm, Olaf

doi:10.48550/arxiv.2212.04513

Cited by 2 publications

(6 citation statements)

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“…The algebraic behaviour of b are essential for proving properties of amplitudes like color-kinematics duality and double copy. [21,[30][31][32] Its failure to be a derivation defines the brackets for the kinetic Lie algebra. We have not examined this in detail for b ′ .…”

Section: Discussionmentioning

confidence: 99%

A Minimal b Ghost

Cederwall

2023

Fortschritte der Physik

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The b ghost, or b operator, used for fixing Siegel gauge in the pure spinor superfield formalism, is a composite operator of negative ghost number, satisfying {q, b} = □, where q is the pure spinor differential (BRST operator). It is traditionally constructed using non-minimal variables. However, since all cohomology has minimal representatives, it seems likely that there should be versions of physically meaningful operators, also with negative ghost number, using only minimal variables. The purpose of this letter is to demonstrate that this statement holds by providing a concrete construction in D = 10 super-Yang-Mills theory, and to argue that it is a general feature in the pure spinor superfield formalism.

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Section: Discussionmentioning

confidence: 99%

A Minimal b Ghost

Cederwall

2023

Fortschritte der Physik

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“…We discuss in detail how these expectations are borne out from the perspective of the homotopy double copy, drawing on the homotopy algebras organising the relevant noncommutative gauge theories that are discussed in [18,19]. We believe that the homotopy algebraic manipulations used to arrive at the slogan (14) are interesting and useful, and further point towards various generalisations of our work.…”

Section: Noncommutative Gauge Theories and Gravitymentioning

confidence: 92%

“…Another question that can be addressed by our result (14) is the extent to which colour-kinematics duality depends on Poincaré invariance. If colour-kinematics duality and the double copy are truly intrinsic properties of certain quantum field theories, they should exist in some form in backgrounds that break spacetime symmetries.…”

Section: Noncommutative Gauge Theories and Gravitymentioning

confidence: 93%

“…Altogether this gives a complete and elegant algebraic formulation of the double copy operations at all levels, which moreover has the potential to elucidate the algebraic origins of colour-kinematics duality [13][14][15], and to give an off-shell non-perturbative definition of the double copy.…”

Section: Homotopy Double Copymentioning

confidence: 99%

“…As such, in this paper we work only with noncommutative field theories at the tree level: when we speak of 'double copy' in this context we mean at the level of tree amplitudes or homotopy algebras at the classical (Lagrangian) level. UV/IR mixing becomes problematic only beyond one-loop, and the double copy operation (14) perhaps offers a different perspective on the non-renormalizability of certain gravitational theories.…”

Section: Noncommutative Gauge Theories and Gravitymentioning

confidence: 99%

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Homotopy Double Copy of Noncommutative Gauge Theories

Szabo,

Trojani

2023

Symmetry

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We discuss the double-copy formulation of Moyal–Weyl-type noncommutative gauge theories from the homotopy algebraic perspective of factorisations of L∞-algebras. We define new noncommutative scalar field theories with rigid colour symmetries taking the role of the zeroth copy, where the deformed colour algebra plays the role of a kinematic algebra; some of these theories have a trivial classical limit but exhibit colour–kinematics duality, from which we construct the double copy theory explicitly. We show that noncommutative gauge theories exhibit a twisted form of colour–kinematics duality, which we use to show that their double copies match with the commutative case. We illustrate this explicitly for Chern–Simons theory, and for Yang–Mills theory where we obtain a modified Kawai–Lewellen–Tye relationship whose momentum kernel is linked to a binoncommutative biadjoint scalar theory. We reinterpret rank-one noncommutative gauge theories as double copy theories and discuss how our findings tie in with recent discussions of Moyal–Weyl deformations of self–dual Yang–Mills theory and gravity.

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Gauge invariant double copy of Yang-Mills theory: the quartic theory

Cited by 2 publications

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A Minimal b Ghost

A Minimal b Ghost

Homotopy Double Copy of Noncommutative Gauge Theories

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