51 research outputs found
Chern-Simons Actions and Their Gaugings in 4D, N=1 Superspace
We gauge the abelian hierarchy of tensor fields in 4D by a Lie algebra. The
resulting non-abelian tensor hierarchy can be interpreted via an equivariant
chain complex. We lift this structure to N=1 superspace by constructing
superfield analogs for the tensor fields, along with covariant superfield
strengths. Next we construct Chern-Simons actions, for both the bosonic and N=1
cases, and note that the condition of gauge invariance can be presented
cohomologically. Finally, we provide an explicit realization of these
structures by dimensional reduction, for example by reducing the three-form of
eleven-dimensional supergravity into a superspace with manifest 4D, N=1
supersymmetry.Comment: 40pp, v2 added reference
Abelian Tensor Hierarchy in 4D, N=1 Superspace
With the goal of constructing the supersymmetric action for all fields,
massless and massive, obtained by Kaluza-Klein compactification from type II
theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of
p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like
invariants. When specialized to the case in which the tensors arise from a
higher-dimensional theory, the invariants may be interpreted as
higher-dimensional Chern-Simons forms reduced to four dimensions. As an
application of the formalism, we construct the eleven-dimensional Chern-Simons
form in terms of four-dimensional, N=1 superfields.Comment: 31 page
Superspace de Rham Complex and Relative Cohomology
We investigate the super-de Rham complex of five-dimensional superforms with
supersymmetry. By introducing a free supercommutative algebra of
auxiliary variables, we show that this complex is equivalent to the
Chevalley-Eilenberg complex of the translation supergroup with values in
superfields. Each cocycle of this complex is defined by a Lorentz- and
iso-spin-irreducible superfield subject to a set of constraints. Restricting to
constant coefficients results in a subcomplex in which components of the
cocycles are coboundaries while the constraints on the defining superfields
span the cohomology. This reduces the computation of all of the superspace
Bianchi identities to a single linear algebra problem the solution of which
implies new features not present in the standard four-dimensional,
complex. These include splitting/joining in the complex and the existence of
cocycles that do not correspond to irreducible supermultiplets of closed
differential forms. Interpreting the five-dimensional de Rham complex as
arising from dimensional reduction from the six-dimensional complex, we find a
second five-dimensional complex associated to the relative de Rham complex of
the embedding of the latter in the former. This gives rise to a second source
of closed differential forms previously attributed to the phenomenon called
"Weyl triviality"
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