  Using the gauge-gravity duality, we investigate the fermionic correlation
function in the D(-1)-D3 brane system which describes the instantonic plasma in
holography. In this system, the charge of the D(-1) brane as the D-instanton
gives the gluon condensate. To simplify the holographic setup, we first reduce
briefly the ten-dimensional supergravity background produced by D(-1)-D3-branes
to an equivalently five-dimensional background. Then using the standard method
for computing the Green function in the AdS/CFT dictionary, we derive the
equations for the fermionic correlation functions and solve them numerically
with the infalling boundary condition. Our numerical results illustrate that
the fermionic correlation function as spectral function includes two branches
of the dispersion curves whose behavior is very close to the results obtained
from the method of hard thermal loop. And the effective mass generated by the
medium effect of fermion splits into two values due to the spin-dependent
interactions induced by instantons. Therefore, this work in holography
demonstrates the instantonic configuration is very influential to the fermionic
plasmino in plasma.
