Remark on the Baryonic Branch of the Warped Deformed Conifold

TL;DR

This paper argues that a superpotential for the entire baryonic branch of the warped deformed conifold likely does not exist, challenging previous suggestions and implications for supersymmetric solutions in the dual supergravity theory.

Contribution

It provides a critical analysis showing the non-existence of a superpotential for the full baryonic branch in the warped deformed conifold context.

Findings

No perturbative superpotential expansion around the known KS superpotential.

Some supersymmetric solutions may not originate from BPS flow equations.

The analysis suggests limitations in the supergravity dual description of the baryonic branch.

Abstract

It has recently been suggested that a superpotential for the baryonic branch of the Klebanov-Strassler field theory (KS) should exist for a sector of the dual supergravity fields. In this note we would like to argue that if extended to cover the whole set of supergravity fields a would-be superpotential does not have a perturbative expansion around the known KS superpotential. Since the family of supergravity duals to the baryonic branch is an expansion around the warped deformed conifold, our argument most likely indicates that there is no such superpotential, and hints that some one-parameter supersymmetric solutions do not arise from BPS flow equations.