Kinematic Algebra from Worldline Vertex Operators

• Applicant: Roberto Bonezzi, Ph.D.
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 524744955

The double copy is a procedure that allows one to obtain gravitational amplitudes from suitable “squares” of gauge theory ones, and is by now an invaluable tool for gravitational calculations. Its foundation is color-kinematics duality, a hidden property of gauge theory amplitudes that is still conjectural beyond tree-level. In particular, its origin from a more fundamental algebraic structure is as of yet obscure. Besides its practical impact, the double copy of scattering amplitudes points at a deep connection between gauge and supergravity theories, which is hardly visible from their usual formulation and deserves to be fully understood. My current research is devoted to attain a first-principle derivation of the double copy and to extend it to fully off-shell and gauge covariant field theories. In this direction, a lot of progress has been made in the past few years by me and my collaborators, as well as other colleagues. The off-shell double copy of Yang-Mills theory has been constructed up to quartic interactions, and unveiled a rich algebraic structure hidden in gauge theories. This is an intricate homotopy algebra, proposed by Reiterer in 2019, which ought to be the off-shell incarnation of the color-kinematics duality observed in amplitudes. This off-shell kinematic algebra, however, is unwieldy to characterize explicitly to all orders and its connection with color-kinematics duality is not yet clear. The main goal of this research proposal is thus to establish the kinematic algebra and its relation to color-kinematics duality in a manageable form. To this end, I plan to show that it can be derived from a simpler structure: the algebra of worldline vertex operators. These are quantum mechanical operators, that I have recently introduced, describing Yang-Mills theory in first quantization. Some preliminary results and related works in string theory strongly suggest that they contain enough structure to achieve this goal. Important applications, which I envision for this project, are the systematic construction of Lagrangians for the double copy and to determine the role of global (super)symmetries in the kinematic algebra of gauge theories.

• DFG Programme: Research Grants