Fermions in an AdS3 Black Hole Background and the Gauge-Gravity Duality

TL;DR

This paper investigates fermionic effects in an AdS3 black hole background, revealing that the dual boundary theory does not experience phase transitions at finite temperature due to fermion-induced modifications.

Contribution

It introduces a model with fermions in AdS3, derives an effective action including Chern-Simons terms, and analyzes the impact on phase transitions via gauge-gravity duality.

Findings

Effective action includes temperature-dependent Chern-Simons terms.

No phase transition occurs at any finite temperature in the presence of fermions.

Numerical analysis of the effective action minimum supports the absence of phase transitions.

Abstract

We study a model whose dynamics is determined by a Maxwell Lagrangian coupled to a complex scalar and a Dirac fermion field, in an $AdS_3$ black hole background. Our study is performed within the context of the Euclidean formalism, in terms of an effective action $S^{eff}$ that results from integrating out the fermion field. In particular, $S^{eff}$ includes an induced parity breaking part which reduces, in the weak coupling limit, to Chern-Simons terms for both the gauge and spin connections, with temperature dependent coefficients. We find numerically the effective action minimum and, applying the AdS/CFT correspondence, we discuss the properties of the dual quantum field theory defined on the boundary. We show that, in contrast with what happens in the absence of fermions, the system does not undergo a phase transition at any finite temperature.