Boundary Conditions and Dirac Fields on AdS$_n$
Claudio Dappiaggi, Andrea Parpinel
TL;DR
This work analyzes massive Dirac fields on $AdS_n$ in both global and Poincaré coordinates, providing a mass-dependent classification of admissible boundary conditions at conformal infinity that ensure the existence of advanced and retarded propagators. It identifies two main classes: the well-known MIT-bag boundary conditions and a broader generalized MIT-bag family, with the generalized class able to support bound states in certain parameter ranges. The authors develop a spectral, boundary-value framework to construct the associated Green's operators and two-point functions, and they illustrate the construction in $PAdS_4$ for both a generalized MIT-bag case (showing a bound state) and the proper MIT-bag case (no bound state), thereby highlighting qualitative differences between the two boundary-condition families. The results provide a principled route to Hadamard states and local quantum field theory on AdS backgrounds with timelike boundaries, with potential applications to AdS/CFT and boundary-dynamics scenarios, and point to avenues for further structural and dynamical analysis of Dirac fields in these spacetimes.
Abstract
We study Dirac fields on AdS$_n$ in both global and Poincaré 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.