Five-dimensional gauge theory and compactification on a torus

Understand

We study five-dimensional minimally supersymmetric gauge theory compactified on a torus down to three dimensions, and its embedding into string/M-theory using geometric engineering.

• The moduli space on the Coulomb branch is hyperkaehler equipped with a metric with modular transformation properties.
• We determine the one-loop corrections to the metric and show that they can be interpreted as worldsheet and D1-brane instantons in type IIB string theory.
• Furthermore, we analyze instanton corrections coming from the solitonic BPS magnetic string wrapped over the torus.