Phases of dual superconductivity and confinement in softly broken N=2 supersymmetric Yang-Mills theories
Jose D. Edelstein, Wifredo Garcia Fuertes, Javier Mas, Juan Mateos Guilarte
TL;DR
This work analyzes confinement in softly broken ${\cal N}=2$ supersymmetric Yang-Mills with off-diagonal couplings among dual ${U}(1)$ factors, focusing on maximal singularities of the quantum moduli space. It derives a Bogomol'nyi bound in the ultrastrong scaling limit and shows BPS vortices exist only when the complex phases of the soft-breaking parameters are aligned; otherwise, vortices are non-BPS and the system exhibits a hybrid Type II dual superconductivity. String tensions for unit vortices follow a deformed universal form $T_k \,\propto \,\Lambda f_N(k)$ with $f_N(k)=|\mu \sin \hat{\theta}_k + \nu \Lambda \sin 2\hat{\theta}_k|$ and $\hat{\theta}_k=k\pi/N$, altering the pattern $T_k$ versus $T_{N-k}$ in general. The paper also reveals half Higgsed vacua supporting superconducting-string solutions and discusses implications for confinement and potential extensions to MQCD and higher Casimir perturbations.
Abstract
We study the electric flux tubes that undertake color confinement in N=2 supersymmetric Yang-Mills theories softly broken down to N=1 by perturbing with the first two Casimir operators. The relevant Abelian Higgs model is not the standard one due to the presence of an off-diagonal coupling among different magnetic U(1) factors. We perform a preliminary study of this model at a qualitative level. BPS vortices are explicitely obtained for particular values of the soft breaking parameters. Generically however, even in the ultrastrong scaling limit, vortices are not critical but live in a "hybrid" type II phase. Also, ratios among string tensions are seen to follow no simple pattern. We examine the situation at the half Higgsed vacua and find evidence for solutions with the behaviour of superconducting strings. In some cases they are solutions to BPS equations.