Quantum Higgs branches of isolated N=2 superconformal field theories

TL;DR

This work identifies quantum Higgs branches that arise at isolated four-dimensional $\mathcal{N}=2$ SCFT points by analyzing Seiberg-Witten curves for $A_n$ and $D_n$ theories. It shows that maximal SCFT points of $SU(n+1)$ and $SO(2n)$ gauge theories host Higgs branches such as $\mathbb{C}^2/\mathbb{Z}_k$ and $\mathbb{C}^2/\mathbb{Z}_2$, whose existence is intrinsic to the SCFT and not visible in the UV-complete gauge theory due to gauging of flavor symmetries. The authors also compute flavor central charges, notably $k_{SU(2)}=\frac{4(n-1)}{n}$ for certain $D_n$ cases, and demonstrate consistency with independent Higgs-branch determinations from BPS quivers and 3d mirror symmetry. These results clarify the structure of isolated $\mathcal{N}=2$ SCFTs and provide a SW-data-driven bridge to other nonperturbative approaches, enriching the understanding of Higgs branches in four-dimensional quantum field theories.

Abstract

We study the Higgs branches of the superconformal points of four-dimensional N=2 super Yang-Mills (SYM) which appear due to the occurrence of mutually local monopoles having appropriate charges. We show, for example, that the maximal superconformal point of SU(2n) SYM has a Higgs branch of the form C^2/Z_n. These Higgs branches are intrinsic to the superconformal field theory (SCFT) at the superconformal point, but do not appear in the SYM theory in which it is embedded. This is because the embedding is a UV extension of the SCFT in which some global symmetry acting on the Higgs branch is gauged irrelevantly. Higgs branches deduced from earlier direct studies of these isolated SCFTs using BPS wall-crossing or 3-d mirror symmetry agree with the ones we find here using just the Seiberg-Witten data for the SYM theories.

Figures (5)

• Figure 1: Branch points $x_i \pm b_{i} \sqrt{\delta}$, denoted by filled blobs, and cycles $A_i$, $B_i$ of the $A_{2k-1}$ theory; $k=4$ in the picture. The dotted arrows show the movements of the branch points under $\delta \to e^{2\pi i}\delta$.
• Figure 2: Branch points and cycles of the $D_{2k+1}$ theory when $m=0$; $k=3$ in the picture. The dotted arrows show the movements of the branch points under $\delta \to e^{2\pi i}\delta$.
• Figure 3: Branch points and cycles of the curve (\ref{['curvealmostdecouple']}) for $n=7$, for $m\ne 0$. The $\hat{A}$ cycle degenerates in the limit $\Lambda \rightarrow \infty$ corresponding to that the U(1) gauge group is decoupled.
• Figure 4: BPS quivers of the superconformal points of the $A$-$D$-$E$ SYM theories.
• Figure 5: 3d mirrors of the $A_{2k-1}$ and $D_{2k}$ theories.