A dual gravity study of the (2+1)D compact U(1) gauge theory coupled with strongly interacting matter fields

We consider the D2-brane probe action in the gravity background dual to N coincident Dp-branes by treating the separation between the D2- and Dp-branes as a non-dynamical parameter for p=2,4,6. The gauge coupling, the core size of a non-BPS instanton and the mass gap of the compact U(1) gauge theory in the D2-brane are determined as a function of the separation in the type IIA gravity region. The results are interpreted in terms of the (2+1)D U(1) gauge theory coupled with the matter fields which are also strongly coupled with the (p+1)D SU(N) gauge field. It is shown that strong coupling of the matter fields to the SU(N) gauge field can drastically modify their screening of the U(1) gauge field. The non-perturbative dependence of the U(1) gauge coupling on the energy scale is obtained.