# Fermions in worldline holography

## TL;DR

This paper explores how the worldline formalism for fermions naturally leads to a holographic description over AdS$_5$, connecting quantum field sources to a higher-dimensional gravitational framework.

## Contribution

It demonstrates that the worldline approach to fermions inherently produces a holographic dual in AdS$_5$, including the proper-time profiles of sources and their relation to renormalization group equations.

## Key findings

- Reconstruction of key holographic models from spin one sources.
- Confirmation of AdS$_5$ as a consistent background for spin two.
- Sources and effective actions satisfy a renormalization group equation.

## Abstract

We analyse the worldline holographic framework for fermions. Worldline holography is based on the observation that in the worldline approach to quantum field theory, sources of a quantum field theory over Mink$_4$ naturally form a field theory over AdS$_5$ to all orders in the elementary fields and in the sources. Schwinger's proper time of the worldline formalism automatically appears with the physical four spacetime dimensions in an AdS$_5$ geometry. The worldline holographic effective action in general and the proper-time profiles of the sources in particular solve a renormalisation group equation. By taking into account sources up to spin one, we reconstruct seminal holographic models. Considering spin two confirms AdS$_5$ as consistent background.