Fiber-Base Duality and Global Symmetry Enhancement

Understand

We show that the 5D Nekrasov partition functions enjoy the enhanced global symmetry of the UV fixed point.

• The fiber-base duality is responsible for the global symmetry enhancement.
• For $SU(2)$ with $N_f\leq 7$ flavors the fiber-base symmetry together with the manifest flavor $SO(2N_f)$ symmetry generate the $E_{N_f+1}$ global symmetry, while in the higher rank case the manifest global symmetry of the two dual theories related by the fiber-base duality map generate the symmetry enhancement.
• The symmetry enhancement at the level of the partition function is manifest once we chose an appropriate reparametrization for the Coulomb moduli.