Instanton Induced Open String Superpotentials and Branes at Singularities

TL;DR

The paper analyzes instanton-induced open-string superpotentials from Euclidean E3-branes in D3/D7 configurations at Abelian orbifold singularities, focusing on consistency with U(1) gauge symmetries and the charged zero-mode structure. It demonstrates how E3 instantons can generate phenomenologically relevant operators such as μ-terms and Yukawas, including scenarios where instantons symbiotically interact with standard gauge instantons to produce multi-instanton contributions. The work also shows that in non-supersymmetric Z_N singularities, E3 instantons can generate non-perturbative scalar couplings, including exponentially suppressed bilinears, even without fermionic operators. Overall, the results provide explicit local and global string constructions where instanton effects lift perturbatively forbidden couplings and offer a framework for exploring SUSY breaking and realistic flavor structures in branes at singularities.

Abstract

We study different aspects of the non-perturbative superpotentials induced by Euclidean E3-branes on systems of D3/D7-branes located at Abelian orbifold singularities. We discuss in detail how the induced couplings are consistent with the U(1) symmetries carried by the D3/D7-branes. We construct different compact and non-compact examples, and show phenomenologically relevant couplings like $μ$-terms or certain Yukawa couplings generated by these E3 instantons. Some other novel effects are described. We show an example where E3-instantons combine with standard gauge instantons to yield new multi-instanton effects contributing to superpotential, along the lines of ref.\cite{geu}. In the case of non-SUSY $Z_N$ tachyon-free singularities it is shown how E3-instantons give rise to non perturbative scalar couplings including exponentially suppressed scalar bilinears.

Figures (1)

• Figure 1: Pictorial view of the instanton $E3^r$ and $D7^{s,t}$-branes going through a singularity where a stack of $D3$-branes are located. The $E3^r-D3$ and $E3^r-D7^{s,t}$ fermionic zero modes ($\eta^r$ and $\eta^{rs}$,$\eta^{rt}$ respectively) are also shown.