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

## TL;DR

This paper provides a detailed derivation of gauge and stringy instanton effects on superpotentials in D3-brane gauge theories at Z_3 orientifold singularities, revealing new non-perturbative contributions.

## Contribution

It offers a microscopic derivation of instanton-generated superpotentials, including gauge and stringy effects, in specific D-brane configurations with detailed conditions for their generation.

## Key findings

- Gauge instantons produce ADS-like superpotentials.
- Stringy instantons generate Majorana masses and non-renormalizable superpotentials.
- Conditions for instanton effects depend on matter content and cycle wrapping.

## 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.