Boundary Conditions and Dirac Fields on AdS$_n$

TL;DR

This paper classifies boundary conditions for Dirac fields on AdS$_n$, extending known classes and constructing propagators and bound states, with explicit examples in four dimensions.

Contribution

It extends the classification of boundary conditions for Dirac fields on AdS$_n$ and constructs explicit propagators and bound states for these conditions.

Findings

Classified boundary conditions ensuring propagator existence

Extended boundary condition families beyond MIT--bag

Constructed explicit propagators and bound states in 4D

Abstract

We study Dirac fields on AdS$_n$ in both global and Poincar\'e charts and, for each mass window, we classify the boundary conditions at conformal infinity that ensure the existence of advanced and retarded propagators. We distinguish the well-known MIT--bag class from a generalized family, thereby extending to arbitrary dimensions the procedure initiated by Blanco. As in the scalar case, we show that suitable generalized boundary data can support bound states. In four dimensions we work out two explicit examples: (i) the MIT case, for which we construct the advanced/retarded propagators and the two-point function of the associated ground state and (ii) a representative generalized boundary condition, for which we construct the propagators and exhibit a normalizable bound state.