Stochastic quantization and holographic Wilsonian renormalization group of massless fermions in AdS

Abstract

We have studied holographic Wilsonian renormalization group (HWRG) of free massless fermionic fields in AdS space and its stochastic quantization (SQ) by identifying the Euclidean action with its boundary on-shell action. The natural extension of the relation between stochastic two-point correlation function and double trace coupling obtained from HWRG computation conjectured in [J.-H. Oh and D. P. Jatkar, J. High Energy Phys. 1211, 144 (2012) arXiv:1209.2242] to fermionic fields is established. We have confirmed that the stochastic two-point function precisely captures the radial flow of the double trace coupling via this relation.