Non-Abelian string junctions as confined monopoles

Abstract

Various dynamical regimes associated with confined monopoles in the Higgs phase of N = 2 two-flavor QCD are studied. The microscopic model we deal with has the SU(2)×U(1) gauge group, with a Fayet-Iliopoulos term of the U(1) factor, and large and (nearly) degenerate mass terms of the matter hypermultiplets. We present a complete quasiclassical treatment of the BPS sector of this model, including the full set of the first-order equations, derivations of all relevant zero modes, and derivation of an effective low-energy theory for the corresponding collective coordinates. The macroscopic description is provided by a CP 1 model with or without twisted mass. The confined monopoles -string junctions of the microscopic theory -are mapped onto BPS kinks of the CP 1 model. The string junction is 1/4 BPS. Masses and other characteristics of the confined monopoles are matched with those of the CP 1 -model kinks. The matching demonstrates the occurrence of an anomaly in the monopole central charge in 4D Yang-Mills theory. We study what becomes of the confined monopole in the bona fide non-Abelian limit of degenerate mass terms where a global SU(2) symmetry is restored. The solution of the macroscopic model is known e.g. from the mirror description of the CP 1 model. The monopoles, aka CP 1 -model kinks, are stabilized by nonperturbative dynamics of the CP 1 model. We explain an earlier rather puzzling observation of a correspondence between the BPS kink spectrum in the CP 1 model and the Seiberg-Witten solution.

Reconnection of non-abelian cosmic strings

“…We find a situation similar to that of Section 4.1, in which the moduli space of vacua is lifted, now at a scale Λ CP N−1 , resulting N different ground states. Recent studies of the lowenergy dynamics of these vortex strings in both supersymmetric theories identify these ground states with the N c vortex strings lying in orthogonal, diagonal U(1) ⊂ U(N c ) subgroups [23]. Once again we have a situation in which the strings reconnect with probability P = 1/N at energy scales E ≪ Λ CP N−1 , and with unit probability at higher energies where the sigma-model becomes asymptotically free and the classical moduli space approximation holds.…”

“…Our model embeds the cosmic string in a non-abelian U(N) gauge theory, so that the string may move in the internal color and flavor space. The formal properties of vortices of this type have been studied extensively of late (see [21][22][23][24]) although, until now, not in the context of cosmic strings. Despite the presence of this internal space we find, rather surprisingly, that cosmic strings continue to reconnect with essentially unit probability, passing through each other only for finely tuned initial conditions.…”

Magnetic impurity inspired Abelian Higgs vortices

“…As a result, it would require infinite energy to break free a bonded pair of a monopole and an anti-monopole placed in a type-II superconductor. This phenomenon, known as the monopole confinement, was proposed by Mandelstam [23,24], Nambu [27], and 't Hooft [40,41], and has served as a profound source of thoughts [33] for the understanding of quark confinement where the underlying Abelian Higgs model platform is extended into various supersymmetric gauge field theory models and the classical Meissner effect is elevated into its supersymmetric versions so that the Nielsen-Olesen magnetic strings become colored ones [3,7,8,10,12,14,15,26,35,36]. See [9,11,21,34,37,38,44,45] for surveys and further literature.…”

Stability analysis of the twisted superconducting semilocal strings

“…Secondly, it describes states with a multicomponent order parameter in condensed matter physics, as for example it the two band superconductivity models or in superfluid systems [6]. Finally, it can be regarded as sector of supersymmetric field theories [7] or as part of one of the Grand Unification Theories that could presumably describe cosmic strings in the early Universe [8]. All this implies that the semilocal model is likely to have interesting physical application, which has inspired considerable interest towards this theory and its solutions.…”