Lens space index and global properties for 4d N = 2 models

TL;DR

This paper investigates the Lens space index of 4d N=2 elliptic models, revealing its sensitivity to global properties and confirming its invariance under S-duality, similar to N=4 theories.

Contribution

It demonstrates that the Lens space index for 4d N=2 elliptic models encodes global properties and remains invariant under S-duality, extending known results from N=4 theories.

Findings

Lens space index detects global properties of N=2 models

Index is invariant under S-duality for these models

Results align with behavior observed in N=4 theories

Abstract

The additional data necessary to univocally fix the gauge group for a given algebra are represented by the same charge lattices of mutually local Wilson and 't Hooft lines for both 4d $\mathcal{N}=4$ SYM and $\mathcal{N}=2$ elliptic models. Motivated by this equivalence in this paper we study the Lens space index of these $\mathcal{N}=2$ elliptic models. The index is indeed sensitive to the global properties and in the $\mathcal{N}=4$ case it is expected to coincide among S-dual models with different global properties, while it gives different results for models that lie in other S-duality orbits. Here by an explicit calculation we show that the same results hold for the $\mathcal{N}=2$ elliptic models as well.