Fermionic pole-skipping in holography

TL;DR

This paper investigates fermionic Green's functions in holographic theories, revealing special points called pole-skipping where the Green's function is not uniquely defined, with implications for quantum chaos and thermal correlators.

Contribution

It identifies and analyzes fermionic pole-skipping points in holography, extending previous bosonic results to fermions and higher dimensions.

Findings

Pole-skipping occurs at specific imaginary Matsubara frequencies and wavenumbers.

Multiple ingoing solutions at the horizon lead to non-uniqueness of Green's functions.

Results are generalized from 3D to higher-dimensional AdS spacetimes.

Abstract

We examine thermal Green's functions of fermionic operators in quantum field theories with gravity duals. The calculations are performed on the gravity side using ingoing Eddington-Finkelstein coordinates. We find that at negative imaginary Matsubara frequencies and special values of the wavenumber, there are multiple solutions to the bulk equations of motion that are ingoing at the horizon and thus the boundary Green's function is not uniquely defined. At these points in Fourier space a line of poles and a line of zeros of the correlator intersect. We analyze these `pole-skipping' points in three-dimensional asymptotically anti-de Sitter spacetimes where exact Green's functions are known. We then generalize the procedure to higher-dimensional spacetimes. We also discuss the special case of a fermion with half-integer mass in the BTZ background. We discuss the implications and possible generalizations of the results.