Fayet-Iliopoulos Terms in AdS/CFT with Flavour

TL;DR

This paper constructs a gravity dual for a field theory with flavor and Fayet-Iliopoulos terms by introducing a constant B field and a D7 brane, revealing noncommutative instanton moduli spaces and matching symmetries.

Contribution

It introduces a holographic model with FI terms via a B field and D7 brane, linking noncommutative instantons to Higgs moduli space in the dual theory.

Findings

The moduli space is described by noncommutative ADHM equations.

The FI term corresponds to an anti-selfdual B field in the gravity dual.

Global symmetries are consistent between the gravity and field theory descriptions.

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.