# Stochastic quantization and holographic Wilsonian renormalization group of free massive fermion

## TL;DR

This paper extends the connection between stochastic quantization and holographic Wilsonian renormalization group to include massive fermions in Euclidean AdS space, confirming the relation with additional boundary terms.

## Contribution

It demonstrates that the stochastic quantization and holographic RG relation applies to massive fermions, with necessary modifications to the bulk action.

## Key findings

- Confirmed the relation for massive fermions in Euclidean AdS
- Identified additional boundary terms needed for fermion actions
- Extended previous work on scalar fields to fermionic case

## Abstract

We extend the relation between stochstic quantization and Holographic Wilsonian Renormalization Group to the massive fermion case in Euclidean AdS space. The original suggestion about the explicit relation between the two theories is in arXiv:1209.2242. To give a fermion bulk action the Dirichlet boundary condition and the Neumann boundary condition, there are some additional terms to the bulk action. We have confirmed that the relation also hold for massive fermion case.