Five-dimensional gauge theories and local mirror symmetry Original Research Article

We study the dynamics of 5-dimensional gauge theory on M4×S1 by compactifying type II/M theory on degenerate Calabi–Yau manifolds. We use the local mirror symmetry and shall show that the prepotential of the 5-dimensional SU(2) gauge theory without matter is given exactly by that of the type II string theory compactified on the local F2 , i.e., Hirzebruch surface F2 lying inside a non-compact Calabi–Yau manifold. It is shown that our result reproduces the Seiberg–Witten theory at the 4-dimensional limit R→0 (R denotes the radius of S1 ) and also the result of the uncompactified 5-dimensional theory at R→∞ .