Vortex Strings and Four-Dimensional Gauge Dynamics
Amihay Hanany, David Tong
TL;DR
This work provides a field-theoretic explanation for the 2D–4D BPS spectrum correspondence observed by Dorey by analyzing vortex strings in the Higgs phase of ${\cal N}=2$ SQCD. The authors show that the exact BPS spectrum of the vortex on the 2D worldsheet reproduces the 4D BPS spectrum, mapping perturbative string excitations to W-bosons and quarks and identifying string kinks with confined monopoles; the central charges and their holomorphic corrections, computed via Seiberg-Witten data in 4D and twisted superpotential in 2D, align precisely. The analysis extends from $N_f=N_c$ to $N_f>N_c$ (semi-local vortices), demonstrating a robust correspondence through RG matching of the vortex FI parameter to the 4D scale $\Lambda$, and highlighting deep links between solitons in the Higgs phase and four-dimensional gauge dynamics.
Abstract
We study the low-energy quantum dynamics of vortex strings in the Higgs phase of N=2 supersymmetric QCD. The exact BPS spectrum of the stretched string is shown to coincide with the BPS spectrum of the four-dimensional parent gauge theory. Perturbative string excitations correspond to bound W-bosons and quarks while the monopoles appear as kinks on the vortex string. This provides a physical explanation for an observation by N. Dorey relating the quantum spectra of theories in two and four dimensions.