Adding flavour to the Polchinski-Strassler background

TL;DR

This paper investigates D7-brane embeddings in the Polchinski-Strassler background with mass deformations, analyzing supersymmetry preservation and meson spectra to understand flavor addition in holography.

Contribution

It generalizes the D7-brane embedding analysis to arbitrary mass values in the Polchinski-Strassler background, including second-order mass effects and supersymmetry verification.

Findings

Embeddings preserve SU(2) x SU(2) symmetry.

Supersymmetry is maintained in the embeddings.

A mass gap appears in the meson spectrum due to adjoint masses.

Abstract

As an extension of holography with flavour, we analyze in detail the embedding of a D7-brane probe into the Polchinski-Strassler gravity background, in which the breaking of conformal symmetry is induced by a 3-form flux G_3. This corresponds to giving masses to the adjoint chiral multiplets. We consider the N=2 supersymmetric case in which one of the adjoint chiral multiplets is kept massless while the masses of the other two are equal. This setup requires a generalization of the known expressions for the backreaction of G_3 in the case of three equal masses to generic mass values. We work to second order in the masses to obtain the embedding of D7-brane probes in the background. At this order, the 2-form potentials corresponding to the background flux induce an 8-form potential which couples to the worldvolume of the D7-branes. We show that the embeddings preserve an SU(2) x SU(2) symmetry. We study possible embeddings both analytically in a particular approximation, as well as numerically. The embeddings preserve supersymmetry, as we investigate using the approach of holographic renormalization. The meson spectrum associated to one of the embeddings found reflects the presence of the adjoint masses by displaying a mass gap.