Fayet-Iliopoulos Terms in AdS/CFT with Flavour

Abstract

We construct the gravity dual of a field theory with flavour in which there are Fayet-Iliopoulos (FI) terms present. For this purpose we turn on a constant Kalb-Ramond B field in four internal space directions of AdS_5 x S^5 together with a D7 brane probe wrapping AdS_5 x S^3. The B field induces noncommutativity on the four internal directions of the D7 brane probe perpendicular to the AdS boundary. We argue on general grounds that the moduli space of the Higgs part of mixed Coulomb-Higgs states in the dual field theory at the boundary is described by the ADHM equations for noncommutative instantons on the four internal directions of the D7 brane probe. In particular, the global symmetries match. The FI term arises as the holographic dual of an anti-selfdual B field. We discuss possible applications for this construction.