Remark on the baryonic branch of the warped deformed conifold

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 oneparameter supersymmetric solutions do not arise from BPS flow equations.

Fake supersymmetry versus Hamilton-Jacobi

“…It would be interesting to apply the above insights to the Hamiltonian system defined by the so-called baryonic branch of the Klebanov-Strassler background [33]. For this system there seems an unsettled issue about the existence of first-order gradient flow equations [34,35].…”

BPS domain walls in $ \mathcal{N}=4 $ supergravity and dual flows

“…This N = 4 theory thus provides the proper framework for a unified, systematic study of the supersymmetry properties of those solutions. Besides giving a genuine supergravity origin to the known superpotentials, working in this setup we will provide a superpotential for the solution of [7], clarifying an issue recently put forward in the literature [12,16].…”

Comments on fake supersymmetry

“…For multiple fields, on the other hand, it was stated for a while that fake susy serves as a genuine restriction in the sense that not all solutions are fake susy. Even after the single scalar result was extended in a natural way to multiple scalars [16], the literature on the topic remained confusing, with papers reporting on flows without a fake susy description [17][18][19][20][21].…”