Democracy from topology
arXiv:2309.04625 · doi:10.1103/PhysRevD.109.066003
Abstract
Chiral form fields in dimensions can be effectively described as edge modes of topological Chern-Simons theories in dimensions. At the same time, manifestly Lorentz-invariant Lagrangian description of such fields directly in terms of a -dimensional field theory is challenging and requires introducing nontrivial auxiliary gauge fields eliminated on-shell with extra gauge symmetries. A recent work by Arvanitakis et al.\ demonstrates (emphasizing the case of 2d chiral bosons) that the two approaches are related, and a peculiar reduction on the -dimensional topological Lagrangian automatically leads to -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 non-chiral 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 11-dimensional supergravity.
arXiv comment7 pages
References in corpus (25)
- Duality Symmetric Actions
- Five-Brane Effective Action In M-Theory
- Covariant Action for a D=11 Five-Brane with the Chiral Field
- On Lorentz Invariant Actions for Chiral P-Forms
- Partial breaking of global D=4 supersymmetry, constrained superfields, and 3-brane actions
- Interacting Chiral Gauge Fields in Six Dimensions and Born-Infeld Theory
- D-brane Charges in Five-brane backgrounds
- Four-Dimensional Avatars of Two-Dimensional RCFT
- Duality-Symmetric Eleven-Dimensional Supergravity and its Coupling to M-Branes
- Self-dual forms: Action, Hamiltonian and Compactification
- Covariant path integral for chiral p-forms
- On Chiral p-Forms
- On Covariant Actions for Chiral Forms
- Three approaches to chiral form interactions
- Self-interacting chiral p-forms in higher dimensions
- Polynomial Duality-Symmetric Lagrangians for Free p-Forms
- Duality-invariant Quantum Field Theories of Charges and Monopoles
- Comments on ABJM free energy on at large and perturbative expansions in M-theory and string theory
- Symmetry-deforming interactions of chiral p-forms
- On duality symmetry in perturbative quantum theory
- Unifying Approaches to Chiral Bosons
- Democratic actions for type II supergravities
- Duality and Fluxes in the Sen Formulation of Self-Dual Fields
- On type IIB supergravity action on solutions
- Partition Functions of Chern-Simons Theory on Handlebodies by Radial Quantization