Supersymmetry Enhancement and Junctions in S-folds

TL;DR

This work investigates how ${\cal N}=3$ theories realized on D3-branes in S-folds can enhance to ${\cal N}=4$ by exploiting string junctions and central charges. It constructs a robust bridge between the S-fold realization and perturbative ${\cal N}=4$ theories, using the perturbative central charge $Z$ to anchor the spectrum and proposing a non-perturbative expression for ${\overline Z}$. Explicit analysis is carried out for ${\mathbb Z}_3$ and ${\mathbb Z}_4$ S-folds, matching to ${\cal N}=4$ theories with $SU(3)$ and $SO(5)$ gauge groups and providing a consistent framework for ${\overline Z}$ via Coulomb moduli and dyonic charges; a heuristic extension to ${\mathbb Z}_6$ and the predicted ${\cal G}_2$ case is discussed. The paper also analyzes walls of marginal stability and highlights how non-perturbative effects shape the BPS spectrum, outlining key open problems in determining ${\overline Z}$ and in mapping marginal deformations.

Abstract

We study supersymmetry enhancement from ${\cal N}=3$ to ${\cal N}=4$ proposed by Aharony and Tachikawa by using string junctions in S-folds. The central charges carried by junctions play a central role in our analysis. We consider planer junctions in a specific plane. Before the S-folding they carry two complex central charges, which we denote by $Z$ and $\bar Z$. The S-fold projection eliminates $\bar Z$ as well as one of the four supercharges, and when the supersymmetry is enhanced $\bar Z$ should be reproduced by some non-perturbative mechanism. For the models of $\mathbb{Z}_3$ and $\mathbb{Z}_4$ S-folds which are expected to give $SU(3)$ and $SO(5)$ ${\cal N}=4$ theories we compare the junction spectra with those in perturbative brane realization of the same theories. We establish one-to-one correspondence so that $Z$ coincides. By using the correspondence we also give an expression for the enhanced central charge $\bar Z$.

Figures (7)

• Figure 1: The $\mathbb{Z}_3$ grading of the lattice $\Gamma_3$ is shown. Red, green, and blue dots represent charges with $F(Q)=0$, $1$ and $2$, respectively.
• Figure 2: Examples of strings in the S-fold and corresponding junctions in the flat background.
• Figure 3: A $\mathbb{Z}_2$ grading of the lattice $\Gamma_4$ is shown. White and black dots represent charges with $F(Q)=0$ and $1$, respectively.
• Figure 4: A $\mathbb{Z}_2$ grading of the lattice with $\tau=(1+i)/2$ is shown. White and black dots represent charges with $0$ and $1$ in $\mathbb{Z}_2$, respectively.
• Figure 5: Examples of strings in the S-fold and corresponding junctions in the orientifold background.