On Supersymmetric D7-branes in the Warped Deformed Conifold

TL;DR

This paper investigates the supersymmetric conditions of D7-branes in the warped deformed conifold, highlighting the necessity of worldvolume flux for supersymmetry preservation and exploring implications for string theory applications.

Contribution

It provides a detailed analysis of supersymmetric D7-branes in warped backgrounds, including numerical construction of fluxes and implications for dual gauge theories.

Findings

Holomorphic embeddings are supersymmetric without flux in unwarped cases.

Most embeddings require worldvolume flux to preserve supersymmetry in warped backgrounds.

Constructed flux configurations numerically for simple embeddings.

Abstract

We study the supersymmetric properties of D7-branes in the warped deformed conifold. We consider the $\kappa$-symmetry conditions on D7-branes in this specific warped background, taking into account the background NS-NS 2-form flux. While any holomorphic embedding defines a supersymmetric D7-brane in the absence of background H-flux, most of the D7-brane embeddings considered in the literature do not preserve supersymmetry for the warped deformed conifold without also including brane worldvolume flux. For the simplest such embedding, we construct numerically the worldvolume fluxnecessary to restore supersymmetry. We also comment on the dual field theory descriptions in terms of cascading N=1 supersymmetric gauge theories with flavors. Finally, we discuss some possible applications of our results to moduli stabilization and vacuum energy uplifting, gauge/gravity duality, and string inflationary model building.