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Gravity = Yang-Mills
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abstract
This essay's title is justified by discussing a class of Yang-Mills-type theories of which standard Yang-Mills theories are special cases but which is broad enough to include gravity as a double field theory. We use the framework of homotopy algebras, where conventional Yang-Mills theory is the tensor product ${\cal K}\otimes \frak{g}$ of a `kinematic' algebra ${\cal K}$ with a color Lie algebra $\frak{g}$. The larger class of Yang-Mills-type theories are given by the tensor product of ${\cal K}$ with more general Lie-type algebras of which ${\cal K}$ itself is an example, up to anomalies that can be cancelled for the tensor product with a second copy $\bar{\cal K}$. Gravity is then given by ${\cal K}\otimes \bar{\cal K}$.
Forward citations
Cited by 3 Pith papers
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The Double Copy of Maximal Supersymmetry in $D=4$
N=8 supergravity to cubic order is realized as the off-shell double copy of N=4 super Yang-Mills, with N=8 supersymmetry and SU(8) R-symmetry emerging from the two gauge factors.
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Off-shell double copy theories in BV
A BV-formalism construction gives off-shell double-copy actions for Chern-Simons, BF, and 2D Yang-Mills theories, with Kodaira-Spencer and Kähler gravity as natural examples.
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HEFT Numerators from Kinematic Algebra
The heavy-mass effective field theory kinematic numerators are derived as the field theory limit of nested commutators of string vertex operators, reproducing and extending earlier fusion-rule results.
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