## SciPost Submission Page

# Charged Quantum Fields in AdS$_2$

### by Dionysios Anninos, Diego M. Hofman, Jorrit Kruthoff

### Submission summary

As Contributors: | Jorrit Kruthoff |

Arxiv Link: | https://arxiv.org/abs/1906.00924v1 |

Date submitted: | 2019-07-29 |

Submitted by: | Kruthoff, Jorrit |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | High-Energy Physics - Theory |

### Abstract

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 $SL(2,\mathbb{R})$ invariant AdS$_2$ geometry endowed with a constant, symmetry preserving background electric field. At large charge the fields oscillate near the AdS$_2$ 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$_2$ 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-matrix. We relate various features displayed by the highly charged particles to the principal series representations of $SL(2,\mathbb{R})$. These representations are unitary and also appear for massive quantum fields in dS$_2$. Both fermionic and bosonic fields are studied. We find that the free charged massless fermion is exactly solvable for general background, providing an interesting arena for the problem at hand.