Non-Supersymmetric SO(3)-Invariant Deformations of N=1* Vacua and their Dual String Theory Description

TL;DR

The paper investigates non-supersymmetric, SO(3)-invariant deformations of $\mathcal{N}=4$ SU($N$) gauge theory using the Polchinski–Strassler construction and identifies the parameter-space region where the low-energy vacuum remains described by dielectric five-branes in a controlled supergravity background. It extends the PS analysis to ${\cal N}=0^*$ directions, derives the effective five-brane potential, and analyzes its critical points, establishing how vacuum structure arises from D5 versus NS5 brane descriptions and how theta-angle dependence alters the dual picture. The work connects to the ${\cal N}=1^*$ massive vacua via the Donagi–Witten integrable system, classifies vacua by index-N subgroups of $\mathbb{Z}_N\times\mathbb{Z}_N$, and shows that the dominant description (Higgs vs confinement) depends on $N$, $g$, and the discrete charges, with a detailed semiclassical analysis at $\theta=0$. The findings clarify the regime of validity for the PS approximation in non-supersymmetric deformations and reveal a rich vacuum landscape with Higgs and confining branches and a theta-angle dependent duality between D5 and NS5 descriptions, bearing on confinement, condensates, and flux tubes in the dual string theory. Overall, the results provide a tractable, holographically grounded framework for studying non-SUSY deformations of ${\cal N}=4$ theories and their IR dynamics, while highlighting the limits of the classical supergravity description and signaling avenues for exploring more complete stringy resolutions near the SU(3) point.

Abstract

We study the SO(3)-invariant relevant deformations of N=4 SU(N) gauge theory using the methods of Polchinski and Strassler. We present the region of parameter space where the non-supersymmetric vacuum is still described by stable ``dielectric'' five branes within the supergravity approximation.

Figures (5)

• Figure 1: Phase structure within PS approximation.
• Figure 2: Supersymmetric potential.
• Figure 3: Phase with only one five brane minimum.
• Figure 4: Phase with two five brane minima.
• Figure 5: Potential at $b=-3$.