Double copy of 3D Chern-Simons theory and 6D Kodaira-Spencer gravity - INSPIRE

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Double copy of 3D Chern-Simons theory and 6D Kodaira-Spencer gravity

Apr 25, 2024

20 pages

Published in:

Phys.Rev.D 110 (2024) 4, 045024

Published: Aug 15, 2024

e-Print:

2404.16830 [hep-th]

DOI:

10.1103/PhysRevD.110.045024 (publication)

Report number:

HU-EP-24/12-RTG

View in:

ADS Abstract Service

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Abstract: (APS)

We apply an algebraic double copy construction of gravity from gauge theory to three-dimensional (3D) Chern-Simons theory. The kinematic algebra

K

is the 3D de Rham complex of forms equipped, for a choice of metric, with a graded Lie algebra that is equivalent to the Schouten-Nijenhuis bracket on polyvector fields. The double copied gravity is defined on a subspace of

K \otimes \bar{K}

and yields a topological double field theory for a generalized metric perturbation and two 2-forms. This local and gauge invariant theory is non-Lagrangian but can be rendered Lagrangian by abandoning locality. Upon fixing a gauge this reduces to the double copy of Chern-Simons theory previously proposed by Ben-Shahar and Johansson. Furthermore, using complex coordinates in

C^{3}

this theory is related to six-dimensional (6D) Kodaira-Spencer gravity in that truncating the two 2-forms and one equation yields the Kodaira-Spencer equations on a 3D real slice of

C^{3}

. The full 6D Kodaira-Spencer theory can instead be obtained as a consistent truncation of a chiral double copy.

Note:

20 pages, published version

space-time: perturbation
dimension: 6
invariance: gauge
dimension: 3
algebra: Lie
metric: perturbation
gravitation
Chern-Simons term
graded
topological

References(47)

Figures(0)

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