Supersymmetric extensions of Kac-Moody boundary conditions in AdS3 gravity

A bstract We extend the Kac-Moody (KM) boundary conditions of AdS 3 gravity by incorporating fermionic fields. For $$ \mathcal{N}=\left(1,1\right) $$ N = 1 1 AdS 3 supergravity, we show that there are two possible ways to implement the fermionic extension. In the first, the extended KM boundary conditions are related to the standard super-Virasoro (VS) boundary conditions through a large gauge transformation realized by the super-Miura map between fields and chemical potentials, establishing a supersymmetric generalization of the KM-VS correspondence. In the second, a more general boundary configuration leads to strong constraints on the fermionic chemical potentials, yet offers a much richer asymptotic structure. It provides us a novel realization of the extended Kac-Moody algebra, and a geometric interpretation in terms of folds in the relativistic free-fermion droplet. Finally, we quantize the latter theory by promoting the classical Poisson brackets to (anti-)commutators, construct the corresponding Hilbert space, and show that the resulting spectrum contains only bosonic soft excitations, with no additional fermionic soft modes.