Holographic Renormalization for Fermions in Real Time

TL;DR

This paper develops a holographic framework for fermions in real-time AdS and Lifshitz spacetimes, deriving propagators, analyzing divergences, and establishing covariant counterterms, advancing the understanding of fermionic fields in holography.

Contribution

It provides explicit solutions for fermionic propagators in real-time holography and derives covariant counterterms for Lifshitz spacetimes, extending previous work to new spacetime geometries.

Findings

Derived fermionic propagators with correct i ε-insertions.

Calculated Euclidean 2-point functions for massless fermions.

Identified divergences and constructed covariant counterterms.

Abstract

We consider the real-time holography on Anti-de-Sitter (AdS) and more generally on Lifshitz spacetimes for spinorial fields. The equation of motion for fermions on general Lifshitz space is derived. Analytically solvable cases are identified. On AdS space we derived time-ordered, time-reversed, advanced and retarded propagators with the correct i \epsilon-insertions. Using the Keldysh-Schwinger contour we also calculated a propagator on thermal AdS. For massless fermions on the Lifshitz spacetime with z=2 we calculated the Euclidean 2-point function and explored the structure of divergences of the on-shell action for general values of z and mass m. The covariant counterterm action is derived.