D-brane Instantons on the T^6/Z_3 orientifold

TL;DR

The work provides a detailed microscopic derivation of nonperturbative superpotentials arising from both gauge (D(-1)) and stringy (ED3) instantons in ${\cal N}=1$ gauge theories living on D3-branes at a ${\mathbb Z}_3$ orientifold. By explicitly constructing and integrating the instanton supermoduli spaces, the authors reproduce ADS-like superpotentials for the ${\cal N}=1$ theories $Sp(6)\times U(2)$ and $U(4)$, and show that ED3-instantons can generate Majorana masses, Yukawa couplings, or nonrenormalizable terms in other quivers. A general ADS analysis is performed to map the allowed matter content that yields such nonperturbative superpotentials, highlighting the dependence on gauge group, representations, and instanton number. The results emphasize the consistency between open-string amplitudes (disk, annulus, Möbius) and the expected field-theory nonperturbative dynamics, and suggest avenues for extending the framework to other singularities and potential phenomenological applications. The study thereby clarifies how local string constructions encode nonperturbative effects in chiral ${\cal N}=1$ theories and provides concrete, computable realizations of ADS and stringy instanton-generated couplings.

Abstract

We give a detailed microscopic derivation of gauge and stringy instanton generated superpotentials for gauge theories living on D3-branes at Z_3-orientifold singularities. Gauge instantons are generated by D(-1)-branes and lead to Affleck, Dine and Seiberg (ADS) like superpotentials in the effective N=1 gauge theories with three generations of bifundamental and anti/symmetric matter. Stringy instanton effects are generated by Euclidean ED3-branes wrapping four-cycles on T^6/\Z_3. They give rise to Majorana masses in one case and non-renormalizable superpotentials for the other cases. Finally we determine the conditions under which ADS like superpotentials are generated in N=1 gauge theories with adjoints, fundamentals, symmetric and antisymmetric chiral matter.