Abstract
We explore the possibilities of breaking conformal symmetry spontaneously by introducing flavour branes into conformal holographic backgrounds in the probe limit. A prototype model of such a mechanism is based on placing D7 - anti-D7 configuration in the Klebanov-Witten conifold based model. In this paper we generalize this model. We conjecture on the required topology of the backgrounds and the corresponding probe brane embeddings. We identify several models that obey these requirements and admit spontaneous breaking of conformal invariance. These include type IIB conifold based examples, dual to defect field theories based on the conifold, and type IIA constructions based on the ABJM model. We identify the dilaton, the corresponding Goldstone boson, discuss its effective action and address the "a-term". We briefly discuss the relevance of these models to the pseudo dilaton.
Highlights
We explore the possibilities of breaking conformal symmetry spontaneously by introducing flavour branes into conformal holographic backgrounds in the probe limit
This and other similar models will be briefly mentioned below when discussing the dilaton action. This configuration is depicted in figure 1. This type of embeddings probe the geometry with gauge branes and the purpose of this paper is to explore flavour branes embeddings
In Sakai-Sugimoto this will not be the case as there is a non-normalizable solution as can be seen from dependency of the UV separation on the merging point. This will not be the case for AdS5 × S5 since, as we reviewed above, the action depends on rmin. This D7-D 7 setup is the only model known to us, which exhibits spontaneous conformal symmetry breaking by introducing a probe flavour D-brane
Summary
We start our journey with a very brief review of the D7 embedding in AdS5×S5 background originally studied in [10, 11]. There was a V-shape solution where the branes do not merge which broke the supersymmetry completely The fact that this model can be dual to a VEV deformation and is not restricted by SUSY makes this a good candidate for conformal symmetry breaking. In Sakai-Sugimoto this will not be the case as there is a non-normalizable solution as can be seen from dependency of the UV separation on the merging point (see 2) This will not be the case for AdS5 × S5 since, as we reviewed above, the (unregulated) action depends on rmin. This D7-D 7 setup is the only model known to us, which exhibits spontaneous conformal symmetry breaking by introducing a probe flavour D-brane (brane and anti-brane). For this setup μ is still a mass parameter and likewise the topology of the embedding is trivial
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