Fiber-Base Duality and Global Symmetry Enhancement

TL;DR

This paper demonstrates that 5D Nekrasov partition functions exhibit enhanced global symmetries at UV fixed points, with fiber-base duality playing a key role in this symmetry enhancement.

Contribution

It reveals how fiber-base duality induces global symmetry enhancement in 5D Nekrasov partition functions, including explicit symmetry groups for various cases.

Findings

Fiber-base duality explains symmetry enhancement in 5D theories.

Enhanced symmetry groups are explicitly identified for different flavor numbers.

Symmetry enhancement is visible through reparametrization of Coulomb moduli.

Abstract

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.