Quantum vortex strings: A review

Abstract

The quantum worldsheet dynamics of vortex strings contains information about the 4d non-Abelian gauge theory in which the string lives. Here I tell this story. The string worldsheet theory is typically some variant of the CP N −1 sigma-model, describing the orientation of the string in a U(N) gauge group. Qualitative parallels between 2d sigma-models and 4d non-Abelian gauge theories have been known since the 1970s. The vortex string provides a quantitative link between the two. In 4d theories with N = 2 supersymmetry, the exact BPS spectrum of the worldsheet coincides with the bulk spectrum in 4d. Moreover, by tuning parameters, the CP N −1 sigmamodel can be coaxed to flow to an interacting conformal fixed point which is related to the 4d Argyres-Douglas fixed point. For theories with N = 1 supersymmetry, the worldsheet theory suffers dynamical supersymmetry breaking and, more interestingly, supersymmetry restoration, in a way which captures the physics of Seiberg's quantum deformed moduli space. Adams Prize Essay

Quantum energies and tensorial central charges of confined monopoles

“…This also explained the observed matching between the BPS spectra of N = (2, 2) CP N −1 models and four-dimensional N = 2 supersymmetric SU(N) gauge theories on the coulomb branch with N f = N [16]. For some recent reviews of these topics see [17][18][19] Dynamical setting. One starts with SU(N c ) N = 2 SQCD with N f massive flavors and N f < 2N c , so that the theory is asymptotically free.…”

“…For this the susy transformations of the fermions have to vanish. Dimensional reduction of the transformations for the fermions in (3.1) gives (no summation over repeated flavor indices) 14 17) where the auxiliary triplet D is understood to be on-shell now, (2.15). The invariance of the gaugino, i.e.…”

“…Though the static background lives in strictly three spatial dimensions, for the purpose of regularization the 17 The given identification corresponds to complex coordinates z = 1 2 (x 1 − i x 2 ).…”

Magnetic impurity inspired Abelian Higgs vortices

“…extract sufficient insight [38,44,45] from exploring a so-called BPS structure after the works of Bogomol'nyi [4] and Prasad and Sommerfeld [32].…”

“…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.…”