Decomposing Instantons in Two Dimensions

Abstract

We study BPS string-like solutions in the 3+1 dimensional gauged CP(1) non-linear sigma model. The same analysis can be applied to study instantons in 2 euclidean dimensions. We use the moduli matrix approach to construct analytically the moduli space and and solve numerically the BPS equations. We identify two topologically inequivalent type of magnetic vortices, which we call S and N vortices. Moreover we discuss their relation to "lump-string" solutions present in the un-gauged case. In particular, we describe how a lump is split into a couple of component S-N vortices after gauging. We extend this analysis to the case of the extended Abelian Higgs model with two flavors, which is known to admit semi-local vortices. When we gauge the relative phase between fields, semi-local vortices are also split into component vortices. We discuss interesting applications of this simple set-up. First, gauging of non-linear sigma models reveals a "partonic" nature of instantons in 1+1 dimensions, an idea long studied also in connection with four dimensional instantons. Second, weak gauging provides for an interesting regularization of the metric of semi-local vortices which preserves supersymmetry and does not lift the moduli space of the string.

Minor changes. 27 pages, 5 figures

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Cited by in corpus (23)

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• Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and $\mathbb{C}{P}^{N-1}$ Lumps
• Classifying BPS States in Supersymmetric Gauge Theories Coupled to Higher Derivative Chiral Models
• Relations among topological solitons
• Fractional Skyrmions and their molecules
• Fractional vortex molecules and vortex polygons in a baby Skyrme model
• Two Species of Vortices in a massive Gauged Non-linear Sigma Model
• Instantons in Chiral Magnets
• Stable $Z$-strings with topological polarization in two Higgs doublet model
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Dissecting zero modes and bound states on BPS vortices in Ginzburg-Landau superconductors
• Spectral Flow of Vortex Shape Modes over the BPS 2-Vortex Moduli Space
• Fractional solitons in non-Euclidian elastic plates
• Exploring instantons with spin-lattice systems
• Spectral wall in collisions of excited Abelian Higgs vortices
• SUSY Chern-Simons ${\mathbb{CP}}^N$ and baby Skyrme models and their BPS structures
• Gauged merons
• Stabilizing semilocal strings by polarization
• Higgs phase in a gauge $\mathbf{U}(1)$ non-linear ${\mathbf{CP}}^1$-model. Two species of BPS vortices and their zero modes
• Sigma Model BPS Lumps on Torus
• Two species of semi-local cosmic strings in Abelian gauged ${\mathbb{CP}}^2$-sigma models coupled to gravity