Scalar effective potential for D7 brane probes which break chiral symmetry

TL;DR

This paper computes the effective scalar potential for D7 brane probes in non-supersymmetric backgrounds, revealing different behaviors in two models and providing insights into chiral symmetry breaking in holographic QCD-like theories.

Contribution

It introduces a method to evaluate the effective potential for D7 branes in non-supersymmetric backgrounds, analyzing stability and chiral symmetry breaking.

Findings

Potential is bounded by 1/Q^4 in the Constable-Myers background.

Higgs potential scales quadratically in the Yang-Mills* background.

Embedding stability is confirmed in both models.

Abstract

We consider D7 brane probes embedded in deformed AdS5 x S5 supergravity backgrounds which are non-supersymmetric in the interior. In the context of the generalised AdS/CFT correspondence, these setups are dual to QCD-like theories with fundamental matter which display chiral symmetry breaking by a quark condensate. Evaluating the D7 action for a surface instanton configuration gives rise to an effective potential for the scalar Higgs vev in the dual field theory. We calculate this potential for two specific supergravity backgrounds. For a metric due to Constable and Myers, we find that the potential is asymptotically bounded by a 1/Q^4 behaviour and has a minimum at zero vev. For the Yang-Mills* background we find that the Higgs potential scales quadratically with the Higgs vev. This corresponds to a canonical mass term and the embedding is again stable.