Non-supersymmetric Meta-stable Vacua from Brane Configurations

TL;DR

The paper constructs type IIA brane configurations with NS, D4, and D6 branes that realize non-supersymmetric meta-stable vacua of 4d ${\rm N}=1$ gauge theories with flavors, and analyzes their lift to M-theory as a reducible M5-brane whose two holomorphic components live in distinct complex structures of a Taub-NUT background. It explains how pseudo-moduli are stabilized not by the holomorphic M5-brane geometry alone but through inter-component interactions and 1-loop field-theory effects, necessitating analyses beyond the brane-probe limit. The authors extend the construction to ${\rm SO/Sp}$ theories, theories with two-index tensor matter, and a chiral gauge theory, illustrating the central ingredients that generate meta-stable vacua in brane systems. These results deepen the dictionary between gauge-theory meta-stability and brane/M-theory geometry, with implications for broader classes of non-supersymmetric vacua and potential connections to branes at singularities.

Abstract

We construct configurations of NS-, D4-, and D6-branes in type IIA string theory, realizing the recently discussed non-supersymmetric meta-stable minimum of 4d N=1 SU(N_c) super-Yang-Mills theories with massive flavors. We discuss their lift to M-theory and the mechanism of pseudo-moduli stabilization. We extend the construction to many other examples of meta-stable minima, including the SO/Sp theories, SU(N_c) with matter in two-index tensor representations, and to a chiral gauge theory.

Figures (8)

• Figure 1: The type IIA brane configurations for $SU(N_c)$ SYM with $N_f$ (massless) flavors (a) and its Seiberg dual theory (b).
• Figure 2: Type IIA brane configuration corresponding to the SUSY breaking minimum.
• Figure 3: The non-supersymmetric type IIA configuration reproducing the non-supersymmetric ISS field theory minimum for arbitrary flavor masses.
• Figure 4: Figure (a) shows the brane configuration describing the supersymmetric minimum of the electric theory. Figure (b) shows the supersymmetry breaking meta-stable vacua in the brane configuration realizing the electric theory.
• Figure 5: Brane configuration describing the $\varphi_0=\tilde{\varphi}_0=0$ point used to estimate the height of the potential barrier.