Holographic Wilsonian flows and emergent fermions in extremal charged black holes

TL;DR

This paper develops a holographic Wilsonian RG framework for charged fermions in AdS backgrounds, revealing fixed points, flow behaviors, and emergent fermionic modes near extremal black holes, aligning with semi-holographic models.

Contribution

It introduces a generalized basis for fermions in holographic RG, explicitly computes flow diagrams in extremal black hole backgrounds, and connects holographic RG to semi-holographic actions.

Findings

RG flows connect UV AdS to IR AdS_2 fixed points.

Double trace operators develop pole singularities at low frequency.

Emergence of light fermionic degrees of freedom near the Fermi surface.

Abstract

We study holographic Wilsonian RG in a general class of asymptotically AdS backgrounds with a U(1) gauge field. We consider free charged Dirac fermions in such a background, and integrate them up to an intermediate radial distance, yielding an equivalent low energy dual field theory. The new ingredient, compared to scalars, involves a `generalized' basis of coherent states which labels a particular half of the fermion components as coordinates or momenta, depending on the choice of quantization (standard or alternative). We apply this technology to explicitly compute RG flows of charged fermionic operators and their composites (double trace operators) in field theories dual to (a) pure AdS and (b) extremal charged black hole geometries. The flow diagrams and fixed points are determined explicitly. In the case of the extremal black hole, the RG flows connect two fixed points at the UV AdS boundary to two fixed points at the IR AdS_2 region. The double trace flow is shown, both numerically and analytically, to develop a pole singularity in the AdS_2 region at low frequency and near the Fermi momentum, which can be traced to the appearance of massless fermion modes on the low energy cut-off surface. The low energy field theory action we derive exactly agrees with the semi-holographic action proposed by Faulkner and Polchinski in arXiv:1001.5049 [hep-th]. In terms of field theory, the holographic version of Wilsonian RG leads to a quantum theory with random sources. In the extremal black hole background the random sources become `light' in the AdS_2 region near the Fermi surface and emerge as new dynamical degrees of freedom.