Holography for fermions

TL;DR

This work develops a holographic description of fermions in a slice of $AdS_5$, deriving an effective boundary action that encodes the 4D spectrum through a boundary correlator $\Sigma(p)$. It presents a 5D/4D dictionary for four regimes split by the bulk mass parameter $ML$, detailing when the external source couples weakly to a CFT, when it mixes and remains light, and when an additional elementary field is required, with a key role played by the operator dimension $\mathrm{Dim}[O_R] = 3/2 + |ML + 1/2|$. The authors show two equivalent holographic descriptions using either a left- or a right-handed source, connected by $M\to -M$ and chirality exchanges, yielding identical spectra. They illustrate the utility with phenomenological applications: generating hierarchical Yukawa couplings and predicting differential running of gauge couplings in holographic GUTs, consistent with explicit 5D KK calculations. Overall, the work provides a practical, calculable framework to analyze fermions in warped extra dimensions via a 5D/4D holographic dictionary.

Abstract

The holographic interpretation is a useful tool to describe 5D field theories in a 4D language. In particular it allows one to relate 5D AdS theories with 4D CFTs. We elaborate on the 5D/4D dictionary for the case of fermions in AdS$_5$ with boundaries. This dictionary is quite useful to address phenomenological issues in a very simple manner, as we show by giving some examples.