Zero sound in effective holographic theories

We investigate zero sound in D -dimensional effective holographic theories, whose action is given by Einstein-Maxwell-Dilaton terms. The bulk spacetimes include both zero temperature backgrounds with anisotropic scaling symmetry and their near-extremal counterparts obtained in 1006.2124 [hep-th], while the massless charge carriers are described by probe D-branes. We discuss thermodynamics of the probe D-branes analytically. In particular, we clarify the conditions under which the specific heat is linear in the temperature, which is a characteristic feature of Fermi liquids. We also compute the retarded Green’s functions in the limit of low frequency and low momentum and find quasiparticle excitations in certain regime of the parameters. The retarded Green’s functions are plotted at specific values of parameters in D = 4, where the specific heat is linear in the temperature and the quasi-particle excitation exists. We also calculate the AC conductivity in D -dimensions as a by-product.