Chern–simons Gauge Theory Coupled With Bf Theory

ABSTRACT. We provide Vasiliev's fully nonlinear equations of motion for bosonic higher spin gauge fields in four spacetime dimensions with an action principle. We first extend Vasiliev's original system with differential forms in degrees higher than one. We then derive the resulting duality-extended equations of motion from a variational principle based on a generalized Hamiltonian sigma-model action. The generalized Hamiltonian contains two types of interaction freedoms:One set of functions that appears in the Q-structure of the generalized curvatures of the odd forms in the duality-extended system; and another set depending on the Lagrange multipliers, encoding a generalized Poisson structure, i.e. a set of polyvector fields of ranks two or higher in target space.We find that at least one of the two sets of interaction-freedom functions must be linear in order to ensure gauge invariance. We discuss consistent truncations to the minimal Type A and B models (with only even spins), spectral flows on-shell and provide boundary conditions on fields and gauge parameters that are compatible with the variational principle and that make the duality-extended system equivalent, on shell, to Vasiliev's original system.

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“…For example, one may consider homotopy charges given by integrals 19) and defined by the equivariant cohomology system…”

Section: A Free Differential Algebras On Non-commutative Base Manifoldsmentioning

confidence: 99%

An action principle for Vasiliev’s four-dimensional higher spin gravity

Boulanger

Sundell

2011

J. Phys. A: Math. Theor.

192

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“…with Q i being the superfield extension of the classical Hamiltonian Q-structure in (29). The locally-defined field configurations form equivalence classes modulo gauge transformations…”

Section: Bv Bracket Induced From Poisson Bracket As Observed By Akszmentioning

confidence: 99%

“…therein); interestingly, the BF model without Poisson structure on a non-commutative manifold was studied in [20,21]. Further developments of the AKSZ formalism can be found in [22,23,24] and [25,26,27,28,29,30,31,32,33], and its close ties to unfolded dynamics have been stressed in [34,35,36,37,38,39]. For related treatments of more general dynamical systems, not necessarily based on differential algebras, see [40,41] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A minimal BV action for Vasiliev’s four-dimensional higher spin gravity

Boulanger

Colombo

Sundell

2012

J. High Energ. Phys.

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ABSTRACT.The action principle for Vasiliev's four-dimensional higher-spin gravity proposed recently by two of the authors, is converted into a minimal BV master action using the AKSZ procedure, which amounts to replacing the classical differential forms by vectorial superfields of fixed total degree given by the sum of form degree and ghost number. The nilpotency of the BRST operator is achieved by imposing boundary conditions and choosing appropriate gauge transitions between charts leading to a globally-defined formulation based on a principal bundle.

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“…After these notes had been completed, we learned that Ikeda [7] had obtained the Courant algebroid-valued sigma model by examining consistent BVdeformations of the abelian Chern-Simons gauge theory coupled with a zero-dimensional BF theory, rather than by immediate application of AKSZ. Also, Hofman and Park [6][5] considered a generalization of the topological open membrane which takes values in a quasi-Lie bialgebroid [10], which is a Courant algebroid with a choice of a splitting.…”

Section: Intro and Brief Historymentioning

confidence: 99%