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Color-Kinematics Duality and Gravitational Waves
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2024 (English)Doctoral thesis, comprehensive summary (Other academic)
Description
Abstract [en]

Recent developments in theoretical physics have led to new insights for gauge theory and gravity scattering amplitudes.The color-kinematics duality, in particular, describes an intriguing set of identities obeyed by the kinematic numerators of gauge-theory scattering amplitudes, mirroring the Jacobi identity of the color factors.  The kinematic Jacobi identities suggest the existence of some unknown kinematic algebra underlying the gauge-theory Feynman rules. However, as of yet, there is no complete Lagrangian construction of duality-satisfying numerators, nor an off-shell realization of a kinematic algebra even for pure Yang-Mills gauge theory. This thesis presents substantial progress on these open problems, first through a Lagrangian whose Feynman rules compute duality-satisfying numerators in the NMHV sector of Yang-Mills theory. In addition, Chern-Simons gauge theory is shown to obey the color-kinematics duality completely off shell, giving rise to a kinematic algebra of volume preserving diffeomorphisms. Similar structures are also identified in the pure-spinor description of super Yang-Mills theory.

The recent detection of gravitational waves by the LIGO/Virgo/KAGRA collaboration, as well as anticipated improvement in sensitivity of future detectors, call for improved precision of the theoretical predictions for binary merger events. Analytical computations involving gravitating and rotating compact objects require both increased classical loop orders in the gravitational coupling as well as the incorporation of spin effects, which have important contributions to the dynamics. For this purpose, an extension of the worldline quantum field theory is presented, based on the effective worldline action of a classical spinning compact object. The formalism is used to compute tree and one-loop amplitudes up to fourth order in spin, and coefficients in the effective worldline action are fixed such that it reproduces known Kerr observables from black hole perturbation theory.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2024. , p. 68
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 2378
Keywords [en]
Quantum field theory, gravitational waves, scattering amplitudes
National Category
Other Physics Topics
Research subject
Theoretical Philosophy
Identifiers
URN: urn:nbn:se:uu:diva-525574ISBN: 978-91-513-2078-6 (print)OAI: oai:DiVA.org:uu-525574DiVA, id: diva2:1846599
Public defence
2024-05-16, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:00 (English)
Opponent
Supervisors
Available from: 2024-04-23 Created: 2024-03-24 Last updated: 2024-04-23
List of papers
1. Off-shell color-kinematics duality for Chern-Simons
Open this publication in new window or tab >>Off-shell color-kinematics duality for Chern-Simons
2022 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 8, article id 035Article in journal (Refereed) Published
Abstract [en]

Many gauge theories possess a hidden duality between color and kinematics in their on-shell scattering amplitudes. An open problem is to formulate an off-shell realization of the duality, thus manifesting a kinematic algebra. We show that 3D Chern-Simons (CS) theory in Lorenz gauge obeys off-shell color-kinematics duality. This holds both for the gauge field and the BRST ghosts, and the duality is manifest in the Feynman rules. A kinematic algebra can be formulated through a second-order differential operator (Poisson bracket) acting on the off-shell fields, and it corresponds to 3D volume-preserving diffeomorphisms, generated by functions in Lorenz gauge. We consider several admissible double-copy constructions of CS theory with Yang-Mills theory, a higher-derivative (DF)(2) gauge theory, or CS theory itself. To obtain non-vanishing amplitudes, we deform pure CS theory by including the maximum amount of adjoint matter that respects the on-shell duality. This gives a new formulation of an N = 4 CS-matter theory, with fields of unusual statistics. We argue that the color-stripped tree amplitudes of this theory are equivalent to those of the Gaiotto-Witten N = 4 CS theory with bi-fundamental matter. We further show that the double copy of the N = 4 CS theory with itself corresponds to maximally supersymmetric N = 8 Dirac-Born-Infeld theory.

Place, publisher, year, edition, pages
Springer NatureSpringer Nature, 2022
Keywords
Scattering Amplitudes, Chern-Simons Theories
National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-482684 (URN)10.1007/JHEP08(2022)035 (DOI)000836240700009 ()
Funder
Knut and Alice Wallenberg Foundation, KAW 2018.0116Knut and Alice Wallenberg Foundation, KAW 2018.0162Swedish Research Council, 621-2014-5722Swedish Research Council, 2018-05973Swedish National Infrastructure for Computing (SNIC), 2018-05973
Available from: 2022-08-29 Created: 2022-08-29 Last updated: 2024-03-24Bibliographically approved
2. 10D super-Yang-Mills scattering amplitudes from its pure spinor action
Open this publication in new window or tab >>10D super-Yang-Mills scattering amplitudes from its pure spinor action
2021 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 12, article id 14Article in journal (Refereed) Published
Abstract [en]

Using the pure spinor master action for 10D super-Yang-Mills in the gauge b0V = QΞ, tree-level scattering amplitudes are calculated through the perturbiner method, and shown to match those obtained from pure spinor CFT techniques. We find kinematic numerators made of nested b-ghost operators, and show that the Siegel gauge condition b0V = 0 gives rise to color-kinematics duality satisfying numerators whose Jacobi identity follows from the Jacobi identity of a kinematic algebra.

Place, publisher, year, edition, pages
Springer NatureSpringer Nature, 2021
Keywords
Scattering Amplitudes, Supersymmetric Gauge Theory, Field Theories in Higher Dimensions
National Category
Subatomic Physics Other Physics Topics
Identifiers
urn:nbn:se:uu:diva-462433 (URN)10.1007/JHEP12(2021)014 (DOI)000728324900003 ()
Funder
EU, European Research Council, ERC-STG-804286 UNISCAMPKnut and Alice Wallenberg Foundation, KAW 2018.0116Knut and Alice Wallenberg Foundation, KAW2018.0162
Available from: 2021-12-23 Created: 2021-12-23 Last updated: 2024-03-24Bibliographically approved
3. Lagrangians manifesting color-kinematics duality in the NMHV sector of Yang-Mills
Open this publication in new window or tab >>Lagrangians manifesting color-kinematics duality in the NMHV sector of Yang-Mills
2023 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 2023, no 8, article id 222Article in journal (Refereed) Published
Abstract [en]

Scattering amplitudes in Yang-Mills theory are known to exhibit kinematic structures which hint to an underlying kinematic algebra that is dual to the gauge group color algebra. This color-kinematics duality is still poorly understood in terms of conventional Feynman rules, or from a Lagrangian formalism. In this work, we present explicit Lagrangians whose Feynman rules generate duality-satisfying tree-level BCJ numerators, to any multiplicity in the next-to-MHV sector of pure Yang-Mills theory. Our Lagrangians make use of at most three pairs of auxiliary fields (2, 1, 0-forms) — surprisingly few compared to previous attempts of Lagrangians at low multiplicities. To restrict the Lagrangian freedom it is necessary to make several non-trivial assumptions regarding field content, kinetic terms, and interactions, which we discuss in some detail. Future progress likely hinges on relaxing these assumptions.

Place, publisher, year, edition, pages
Springer, 2023
Keywords
Scattering Amplitudes, Duality in Gauge Field Theories
National Category
Other Physics Topics
Identifiers
urn:nbn:se:uu:diva-524486 (URN)10.1007/JHEP08(2023)222 (DOI)001188238100001 ()
Funder
Knut and Alice Wallenberg Foundation, KAW 2018.0116Knut and Alice Wallenberg Foundation, KAW 2018.0162Ragnar Söderbergs stiftelse
Available from: 2024-03-05 Created: 2024-03-05 Last updated: 2024-04-09Bibliographically approved
4. Scattering of spinning compact objects from a worldline EFT
Open this publication in new window or tab >>Scattering of spinning compact objects from a worldline EFT
2024 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 2024, no 3, article id 108Article in journal (Refereed) Published
Abstract [en]

We study the EFT of a spinning compact object and show that with appropriate gauge fixing, computations become amenable to worldline quantum field theory techniques. We use the resulting action to compute Compton and one-loop scattering amplitudes at fourth order in spin. By matching these amplitdes to solutions of the Teukolsky equations, we fix the values of Wilson coefficients appearing in the EFT such that it reproduces Kerr black hole scattering. We keep track of the spin supplementary condition throughout our computations and discuss alternative ways to ensure its preservation.

Place, publisher, year, edition, pages
Springer, 2024
National Category
Other Physics Topics
Identifiers
urn:nbn:se:uu:diva-525573 (URN)10.1007/jhep03(2024)108 (DOI)
Funder
Knut and Alice Wallenberg Foundation, KAW 2018.0116Knut and Alice Wallenberg Foundation, KAW 2018.0162
Available from: 2024-03-24 Created: 2024-03-24 Last updated: 2024-03-25Bibliographically approved

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