N=2 Superconformal Field Theory with ADE Global Symmetry on a D3-brane Probe

TL;DR

This paper investigates mass deformations of N=2 superconformal field theories with ADE global symmetries on D3-branes, constructing Seiberg-Witten curves and differentials, revealing universal features of global symmetries in these theories.

Contribution

It provides explicit Seiberg-Witten curves and differentials for ADE symmetric N=2 SCFTs, demonstrating the universality of physical results across different residue representations.

Findings

Seiberg-Witten curves determined by Type IIB 7-brane backgrounds.

Residues of Seiberg-Witten differentials transform under ADE groups.

Physical results are independent of the choice of residue representation.

Abstract

We study mass deformations of N=2 superconformal field theories with ADE global symmetries on a D3-brane. The N=2 Seiberg-Witten curves with ADE symmetries are determined by the Type IIB 7-brane backgrounds which are probed by a D3-brane. The Seiberg-Witten differentials $\lambda$ for these ADE theories are constructed. We show that the poles of $\lambda$ with residues are located on the global sections of the bundle in an elliptic fibration. It is then clearly seen how the residues transform in an irreducible representation of the ADE groups. The explicit form of $\lambda$ depends on the choice of a representation of the residues. Nevertheless the physics results are identical irrespective of the representation of $\lambda$. This is considered as the global symmetry version of the universality found in N=2 Yang-Mills theory with local ADE gauge symmetries.