Abstract
By using integral forms we derive the superspace action of D=3, N=1 supergravity as an integral on a supermanifold. The construction is based on target space picture changing operators, here playing the role of Poincare' duals to the lower-dimensional spacetime surfaces embedded into the supermanifold. We show how the group geometrical action based on the group manifold approach interpolates between the superspace and the component supergravity actions, thus providing another proof of their equivalence.
Highlights
The construction is based on target space picture changing operators, here playing the role of Poincare duals to the lower-dimensional spacetime surfaces embedded into the supermanifold
We show how the group geometrical action based on the group manifold approach interpolates between the superspace and the component supergravity actions, providing another proof of their equivalence
JHEP10(2016)049 cannot be integrated on a supermanifold SM(n|m) since there is no top form in the usual complex of differential forms
Summary
In the case of superspace (see for example the textbook [1]), the Lagrangian is a superfield F (x, θ), a local functional of the superfields φ(x, θ) of the theory. Given (2.2), one can compute the Berezin integral by expanding the action in powers of θ and selecting the highest term. In the case of rigid supersymmetry, the action is invariant because the variation of the Lagrangian is a total derivative. There are several advantages in having a superspace action as in (2.2) It is the most economical and compact way to describe the complete action for all physical degrees of freedom of supergravity, it encodes all symmetries, it provides a powerful quantization technique, known as supergraph method, which minimises the amount of Feymann diagrams needed for a single scattering amplitude. In that respect the group-manifold approach seems to overcome these problems
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