Supersymmetric minisuperspace models in self-dual loop quantum cosmology

A bstract In this paper, we study a class of symmetry reduced models $$ \mathcal{N} N = 1 super- gravity using self-dual variables. It is based on particular Ansatz for the gravitino field as proposed by D’Eath et al. We show that essential part constraint algebra in classical theory closes. particular, (graded) Poisson bracket between left and right supersymmetry reproduces Hamiltonian constraint. For quantum theory, apply techniques from manifestly supersymmetric approach to loop supergravity, which yields graded analog holonomy-flux natural state space. implement remaining constraints theory. certain subclass these models, explicitly commutator exactly relations. trace Hamilton operator. Finally, consider dynamics compare it quantization standard variables minisuperspace techniques.