For Legendrian submanifolds whose Rabinowitz Floer complex are acyclic we establish a relative Calabi-Yau structure as defined by Brav-Dyckerhoff, that can be seen as a generalisation of Sabloff duality for linearised legendrian contact homology. More precisely, the relative Calabi-Yau structure holds for the DG-morphism given by the inclusion of the DGA of chains on the based loop space of the Legendrian into the Chekanov-Eliashberg algebra of the same, with coefficients in the same DGA. Under certain conditions this can be used to show that the augmentation variety is a holomorphic Lagrangian.
This is joint work with N. Legout.