Uplifting GPPZ: A Ten-dimensional Dual of $\mathcal{N}=1^{*}$

TL;DR

This work constructs a precise ten-dimensional Type IIB supergravity background by uplifting the five-dimensional GPPZ flow, thereby modeling the $\mathcal{N}=1^{*}$ deformation of $\mathcal{N}=4$ SYM. The uplift relies on a consistent truncation of the $5d$ $\mathcal{N}=8$ SO$(6)$ gauged supergravity to a four-real-scalar sector and explicit uplift formulae, yielding an explicit warped metric and full NS-NS/R-R fluxes while preserving an $SO(3)$ flavor symmetry. The ten-dimensional solution is singular in the IR, controlled by an integration constant $\lambda$ that encodes the gaugino condensate-to-mass ratio; holographic criteria restrict $|\lambda|\le 1$, with $\lambda=1$ highlighted as physically significant for a supersymmetric vacuum, though the full interpretation remains subtle. The paper provides a concrete realization of the Polchinski–Strassler scenario in a tractable analytic setting and outlines avenues to resolve the singularities or extend to other $\mathcal{N}=1^{*}$ vacua via larger truncations and alternative IR completions.

Abstract

We find a new supersymmetric solution of type IIB supergravity which is the uplift of the GPPZ solution of maximal SO$(6)$ gauged supergravity in five dimensions. This background is expected to be holographically dual to an $\mathcal{N}=1^{*}$ supersymmetric mass deformation of four-dimensional $\mathcal{N}=4$ SYM. The ten-dimensional solution is singular in the region corresponding to the IR regime of the dual gauge theory and we discuss the physics of the singularity in some detail.