Boundary Conditions in Anti-de Sitter Spacetime

Boundary conditions of field theories in anti-de Sitter (AdS) spacetime is essential to our understanding of field dynamics in AdS. In this work, we build upon the formalism of Ishibashi & Wald (2004), which systematically examined and classified the boundary conditions for scalar field theory, Maxwell theory, as well as linearized gravity in AdS that give well-posed dynamics. We show that in the electromagnetic and gravitational cases in four-dimensional spacetime, there are precisely two local boundary conditions that preserve the full AdS symmetry. In the gravitational case, one of these conditions corresponds to boundary conditions previously given in the 1980s by Ashtekar and Magnon (1984) and by Henneaux and Teitelboim (1985). The alternative boundary conditions allow for a change in the conformal geometry on the AdS boundary. We elucidate the properties of these alternative boundary conditions.