Quantum vortex strings: A review
By David Tong. 2008
182 citations recorded by the source corpus.
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 sigma-model 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.
Subfields: Geometry and Topology, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/ae6756c9ca71eb046c4bfaaff11ec89e2b18a4f6
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In Geometry and Topology
In Nuclear and High Energy Physics
Citations in the corpus
- Wall-crossing in coupled 2d-4d systems (2011, background): “We assume that T2d has a compact global symmetry group G and moreover we assume that in isolation T2d has a finite number of massive vacua, labeled i ∈ V[S].2 The G-symmetry can then be gauged by coupling to a G-gauge theory in T4d.”
- Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry (2009, unknown): “Before we start, we should mention a relationship between our consideration of the surface operators and the analysis of quantum vortices in the Higgs phase of N = 2 theories presented in the review [15] and references therein.”