Holographic spectroscopy of fermion with instantons

Abstract

Using the gauge-gravity duality, we investigate the fermionic spectroscopy in the D(-1)-D3 brane system. The background geometry of this system described by IIB supergravity includes a black (deconfined) and bubble (confined) D3-brane which corresponds respectively to a deconfined and a confined gauge theory in holography. The charge of the D(-1) brane as the D-instanton gives the gluon condensate in this model. 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 the fermionic spectrum in the confined case is obtained by decomposing the fermion with dimensional reduction. In addition, by 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 in the deconfined case 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. In the confined case, the holographic correlation function indicates several separated dispersion curves which illustrates consistently the onset mass in the fermionic spectrum we obtained. Therefore, this work in holography demonstrates the instantonic configuration is very influential to the fermion in QCD.