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

TL;DR

<3-5 sentences high-level summary>We study mass deformations of $N=2$ superconformal theories with ADE global symmetry realized on a D3-brane probe in a Type IIB 7-brane background. The authors construct the Seiberg-Witten curves and meromorphic differentials by identifying global sections of the elliptic fibration and show that the poles carry residues transforming in irreducible representations of the ADE groups; crucially, the resulting physics is independent of the chosen representation. They demonstrate a universal structure under RG flows, show how fixed-point $E_n$ theories flow to Lagrangian $D_4$ and $A$-type theories, and verify universality with numerical checks and flows to $N_f eq 4$ $SU(2)$ QCD. The work connects ADE global symmetry in F-theory settings to the universal aspects of SW periods and suggests a deeper link to Mordell-Weil lattices and BPS spectra in these non-Lagrangian fixed points.

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 $λ$ for these ADE theories are constructed. We show that the poles of $λ$ 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 $λ$ depends on the choice of a representation of the residues. Nevertheless the physics results are identical irrespective of the representation of $λ$. This is considered as the global symmetry version of the universality found in N=2 Yang-Mills theory with local ADE gauge symmetries.

Figures (2)

• Figure 1: Dynkin diagrams
• Figure 2: The period $a=\int_\alpha \lambda^{A_2}_{f}$ in the fundamental of $SU(3)$ is plotted for $z=10,\; m_1=2 x -0.2\, i, \; m_2=-0.4+1.5\, i\, x$ .