Democratic Lagrangians from topological bulk

Abstract

Chiral form fields in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>d</a:mi></a:math> dimensions can be effectively described as edge modes of topological Chern-Simons theories in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>d</c:mi><c:mo>+</c:mo><c:mn>1</c:mn></c:math> dimensions. At the same time, manifestly Lorentz-invariant Lagrangian description of such fields directly in terms of a <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>d</e:mi></e:math>-dimensional field theory is challenging and requires introducing nontrivial auxiliary gauge fields eliminated on shell with extra gauge symmetries. A recent work by Arvanitakis demonstrates (emphasizing the case of 2d chiral bosons) that the two approaches are related, and a peculiar reduction on the (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>d</g:mi><g:mo>+</g:mo><g:mn>1</g:mn></g:mrow></g:math>)-dimensional topological Lagrangian automatically leads to <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>d</i:mi></i:math>-dimensional Lagrangians with appropriate sets of auxiliary fields. We develop this setup in three distinct directions. First, we demonstrate how arbitrary Abelian self-interactions for chiral forms can be included using nonlinear boundary terms in the Chern-Simons theory. Second, by generalizing the Chern-Simons theory to the BF-theory, we obtain an analogous democratic description of nonchiral form fields, where electric and magnetic potentials appear as explicit dynamical variables. Third, we discuss the effects of introducing topological interactions in the higher-dimensional bulk, which produce extra interaction terms in the boundary theory. When applied to a topological 4-form field in 12 dimensions, this construction results in a democratic description of the 3-form gauge field of the eleven-dimensional supergravity. Published by the American Physical Society 2024

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