Holographic derivation of a class of short range correlation functions

Abstract: We construct a class of backgrounds with a warp factor and anti-de Sitter asymptotics, which are dual to boundary systems that have a ground state with a short-range two-point correlation function. The solutions of probe scalar fields on these backgrounds are obtained by means of confluent hypergeometric functions. The explicit analytical expressions of a class of short-range correlation functions on the boundary and the correlation lengths $\xi$ are derived from gravity computation. The two-point function calculated from gravity side is explicitly shown to exponentially decay with respect to separation in the infrared. Such feature inevitably appears in confining gauge theories and certain strongly correlated condensed matter systems.