Double Copy from Tensor Products of Metric BV${}^{■}$-algebras

Abstract

Field theories with kinematic Lie algebras, such as field theories featuring colour-kinematics duality, possess an underlying algebraic structure known as BV${}^{■}$-algebra. If, additionally, matter fields are present, this structure is supplemented by a module for the BV${}^{■}$-algebra. We explain this perspective, expanding on our previous work and providing many additional mathematical details. We also show how the tensor product of two metric BV${}^{■}$-algebras yields the action of a new syngamy field theory, a construction which comprises the familiar double copy construction. As examples, we discuss various scalar field theories, Chern-Simons theory, self-dual Yang-Mills theory, and the pure spinor formulations of both M2-brane models and supersymmetric Yang-Mills theory. The latter leads to a new cubic pure spinor action for ten-dimensional supergravity. We also give a homotopy-algebraic perspective on colour-flavour-stripping, obtain a new restricted tensor product over a wide class of bialgebras, and we show that any field theory (even one without colour-kinematics duality) comes with a kinematic $L_{\infty }$-algebra.

v3: 98 pages, references added, typos fixed, version published in Fortschritte der Physik

References in corpus (43)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• New Relations for Gauge-Theory Amplitudes
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Fractional M2-branes
• Minimal Basis for Gauge Theory Amplitudes
• Black holes and the double copy
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• Yang-Mills origin of gravitational symmetries
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism
• 5 loops in 24/5 dimensions
• A double copy for $\mathcal{N}=2$ supergravity: a linearised tale told on-shell
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• Double Copy from Homotopy Algebras
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization
• Constraints and Generalized Gauge Transformations on Tree-Level Gluon and Graviton Amplitudes
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Heterotic Kerr-Schild Double Field Theory and Classical Double Copy
• Double Field Theory as the Double Copy of Yang-Mills
• Y-formalism and $b$ ghost in the Non-minimal Pure Spinor Formalism of Superstrings
• Kinematic Lie Algebras From Twistor Spaces
• Superfield actions for N=8 and N=6 conformal theories in three dimensions
• Gauge invariant double copy of Yang-Mills theory: the quartic theory
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• Loop Amplitudes and Quantum Homotopy Algebras
• Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket
• Why is the Weyl double copy local in position space?
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Metric 3-Lie algebras for unitary Bagger-Lambert theories
• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• Beta-gamma systems and the deformations of the BRST operator
• Field Theory Equivalences as Spans of $L_{\infty }$-algebras

Cited by in corpus (4)

• The double copy effective action: a quantum (chromodynamics) approach to space-time
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• Ersatz gravity and black-hole thermodynamics from Manin gauge theory with noncompact gauge group
• Extremal Black Holes from Homotopy Algebras