Mode solutions for a Klein-Gordon field in anti–de Sitter spacetime with dynamical boundary conditions of Wentzell type

Abstract

We study a real, massive Klein-Gordon field in the Poincaré fundamental domain of the (d þ 1)-dimensional anti-de Sitter (AdS) spacetime, subject to a particular choice of dynamical boundary conditions of generalized Wentzell type, whereby the boundary data solves a nonhomogeneous, boundary Klein-Gordon equation, with the source term fixed by the normal derivative of the scalar field at the boundary. This naturally defines a field in the conformal boundary of the Poincaré fundamental domain of AdS. We completely solve the equations for the bulk and boundary fields and investigate the existence of bound state solutions, motivated by the analogous problem with Robin boundary conditions, which are recovered as a limiting case. Finally, we argue that both Robin and generalized Wentzell boundary conditions are distinguished in the sense that they are invariant under the action of the isometry group of the AdS conformal boundary, a condition which ensures in addition that the total flux of energy across the boundary vanishes.

Ground states of a Klein-Gordon field with Robin boundary conditions in global anti–de Sitter spacetime

“…In this respect it would be interesting to consider on CAdS n more general scenarios, such as dynamical boundary conditions which have been recently studied in the Poincaré patch in [24] and in [25] from a rigorous viewpoint.…”

Quantum field theory on global anti-de Sitter space-time with Robin boundary conditions

“…Even in this simplified model, there are many variations to consider. First of all, the properties of the QFT of the scalar field depend on whether one considers global AdS [2,[4][5][6]9,11,15,16] or the Poincaré patch PAdS [12][13][14][26][27][28], the latter being particularly relevant in the context of the AdS/CFT correspondence. In both cases, the fact that AdS is not a globally hyperbolic space-time means that, in order to have a well-defined QFT, appropriate boundary conditions must be applied to the field at null infinity, which is a time-like surface [5,[13][14][15][29][30][31][32].…”

Thermal expectation values of fermions on anti-de Sitter space-time

“…Quantum field theory on adS has been studied for many years, starting with the seminal work in [28], where a quantum scalar field is considered and the nonrotating vacuum state constructed. Quantum field theory on adS is complicated by the presence of the time-like boundary at infinity, on which boundary conditions must be imposed [28][29][30][31][32][33]. For a quantum scalar field, applying either Dirichlet [28,[34][35][36] or Neumann [28,34,37] boundary conditions yields a global vacuum state which, like the global Minkowski vacuum, respects the maximal symmetry of the underlying adS space-time.…”