Notes on Enhancement of Flavor Symmetry and 5d Superconformal Index

TL;DR

This paper investigates the enhancement of flavor symmetry in 5d SU(2) gauge theories with various flavors by analyzing superconformal indices, providing evidence for symmetry enhancement and connections to geometric structures.

Contribution

It offers detailed computations of superconformal indices for SU(2) theories with 0 and 1 flavors, supporting flavor symmetry enhancement and linking to F_2 geometry.

Findings

Evidence for E_{N_f+1} flavor symmetry enhancement

Superconformal index computations support conjectured symmetry

Connection between F_2 geometry and E_1 superconformal field theory

Abstract

The UV fixed point theory of SU(2) gauge theory with N_f = 0,1,...,7 flavors is believed to have the enlarged E_{N_f +1} flavor symmetry. Actually it is not easy to check this conjecture because the UV theory is strongly-coupled, however, computation of certain SUSY protected quantities provides strong evidence for the enhancement of flavor symmetry. We study the superconformal index for SU(2) gauge theory with N_f = 0, 1 flavors in details, and we give a support for the enhancement by studying combinatorial structure of the superconformal indexes of these theories. We also give a nontrivial evidence that the local F_2 geometry leads to the E_1 superconformal field theory.