nLab
rheonomy modality

In higher supergeometry the bosonic modality ()\stackrel{\rightsquigarrow}{(-)} which sends supermanifolds to their underlying ordinary bosonic smooth manifolds has a further right adjoint Rh\Rh, see at super smooth infinity-groupoid.

This means that if Fields\mathbf{Fields} is a moduli stack of fields, for instance for supergravity, then Rh(Fields)Rh(\mathbf{Fields}) is such that for X^\hat X any supermanifold with underlying manifold XX^X \to \hat X, then maps

X^Rh(Fields) \hat X \longrightarrow Rh(\mathbf{Fields})

are equivalently maps

XFields X \longrightarrow \mathbf{Fields}

hence are fields configurations on the underlying ordinary manifold XX.

In the supergeometry formulation of supergravity this is what goes into the rheonomy superspace constraint which demands that on-shell super-field configurations X^Fields\hat X \to \mathbf{Fields} have to be uniquely determined by their restriction along XX^X \to \hat X. Therefore the space Rh(Fields)Rh(\mathbf{Fields}) contains the rheonomic field configurations among all the field configurations modulated by Fields\mathbf{Fields}.

Revised on June 3, 2015 04:48:22 by David Corfield (129.12.18.235)