Fermionic Open EFT from Holography
Abstract
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 AdSd+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.