Charged quantum fields in AdS₂

We consider quantum field theory near the horizon of an extreme Kerr black hole. In this limit, the dynamics is well approximated by a tower of electrically charged fields propagating in an SL(2,R) S L ( 2 , ℝ ) invariant AdS _2 2 geometry endowed with a constant, symmetry preserving background electric field. At large charge the fields oscillate near the AdS _2 2 boundary and no longer admit a standard Dirichlet treatment. From the Kerr black hole perspective, this phenomenon is related to the presence of an ergosphere. We discuss a definition for the quantum field theory whereby we ‘UV’ complete AdS _2 2 by appending an asymptotically two dimensional Minkowski region. This allows the construction of a novel observable for the flux-carrying modes that resembles the standard flat space S S -matrix. We relate various features displayed by the highly charged particles to the principal series representations of SL(2,R) S L ( 2 , ℝ ) . These representations are unitary and also appear for massive quantum fields in dS _2 2 .