Fermionic pole-skipping in holography

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 and derive the generic form the boundary correlator takes near the pole-skipping points in momentum space. 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.

Pole-skipping of scalar and vector fields in hyperbolic space: conformal blocks and holography

“…This study also allows us to uncover some features of how the poleskipping phenomenon manifests itself when the field theory lives in a curved space. For some other recent studies regarding pole-skipping, see [36][37][38][39][40][41].…”

“…As a consequence, the corresponding Green's function becomes ill-defined at this special point. It was later observed that pole-skipping also occurs in other sectors of gravitational perturbations, and also for scalar, vector and fermionic fields, being always related to a special property of the near-horizon equations of motion [30][31][32][33]40]. All these studies considered the case of planar black holes, in which the perturbations can be decomposed in terms of plane waves.…”

“…It would be interesting to generalize our work to other fields such as fermion and antisymmetric tensor fields. For example, the pole-skipping points of fermion fields were studied by holography in [40]. It is also interesting to investigate the pole-skipping phenomena in QFTs without conformal symmetry.…”

Quasinormal modes in charged fluids at complex momentum

“…Holographically, it has been studied mainly for the Schwarzschild black hole [22,24] as well as for a neutral black hole that explicitly breaks translation invariance [23]. The fermionic case was considered in [25]. From the field theory perspective, this phenomenon was investigated in [26] for effective field theories and in [27] for conformal field theories with large central charge.…”

Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential

“…However the resultant pole-skipping points in such cases lie totally in the lower half of Imw − Imq plane. See also[64][65][66][67][68][69][70][71][72][73][74].…”