  In this work we initiate the study of open effective field theories of
fermions interacting with holographic baths. As a first step in this direction,
we explain how the recently identified holographic Schwinger-Keldysh saddles
naturally reproduce the Fermi-Dirac statistics of boundary correlators. We
study Dirac fermions propagating in the background of a doubled $AdS_{d+1}$
Schwarzchild blackbrane. We solve for both ingoing (quasi-normal) as well as
outgoing (Hawking) modes of the Dirac field in a boundary gradient expansion
and compare our findings against exact results in $d=2$. The holographic
Schwinger-Keldysh boundary conditions automatically select a unique combination
of these modes consistent with fermionic KMS relations. Evaluating the bulk
on-shell action using these solutions, we obtain an explicit expression for the
influence phase of the probe fermion in a gradient expansion.
