Vortex Condensates¶for the SU(3) Chern–Simons Theory

By M. Nolasco, G. Tarantello. 2000

136 citations recorded by the source corpus.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e6bf390c068f5fc2bc2f46214cfe00389b5094ef

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Citations in the corpus

Sharp estimates for solutions of multi‐bubbles in compact Riemann surfaces (2002, unknown): “By using some special variational scheme, Struwe and Tarantello [37] were able to obtain nontrivial solutions of (1.1) for 8π ρ 4π 2 when h ≡ 1 and M is the flat torus with fundamental domain [0, 1] × [0, 1].”
Non-Topological Multi-Vortex Solutions to the Self-Dual Chern-Simons-Higgs Equation (2002, background): “5) and recent developments of related subjects, we refer the readers to Hong-Kim-Pac [8], Jackiw-Weinberg [9], Wang [17], Spruck-Yang [14], Caffarelli-Yang [2], Tarantello [16], Chae-Imanuvilov [3], Nolasco-Tarantello [12, 13], Yang [18] and the references therein.”
Elliptic functions, Green functions and the mean field equations on tori (2006, background): “It also comes from statistical physics as the mean field limits of the Euler flow, hence the name.”
Classification and nondegeneracy of SU(n+1) Toda system with singular sources (2011, methodology): “For example, in the Chern-Simons theory, the Liouville equation is related to abelian gauge field theory, while the Toda system is related to nonabelian gauge, see [11], [12], [14], [21], [22], [30], [31], [32], [36], [37] and references therein.”
Classification of blowup limits for SU(3) singular Toda systems (2013, methodology): “MR 2001e:58022 Zbl 0951.58030 [Nolasco and Tarantello 2000] M. Nolasco and G. Tarantello, “Vortex condensates for the SU(3) Chern–Simons theory”, Comm. Math.”
Topological degree for a mean field equation on Riemann surfaces (2003, background): “For the mathematical theory of the relativistic Chern-SimonsHiggs model, see [4, 21, 22, 34, 35, 37, 39, 40, 41] and the references therein.”
Some existence results for the Toda system on closed surfaces (2007, background): “In [23], [25] and [26] some existence results are given and it is proved that if hi ≡ 1 and if some additional assumptions are satisfied, then (0, 0) is a local minimizer for Jρ, so the functional has a mountain pass structure and some corresponding critical points.”
Profile of Blow-up Solutions to Mean Field Equations with Singular Data (2004, background): “In this situation aj 2 N for j ¼ 1; 2; . . . ;m, and mean field equations with singular data also play an important role for the understanding of the bubbling phenomenon of the Toda system (Jost and Wang, 2001) or the SUðN þ 1Þ Chern–Simons theory (Nolasco and Tarantello, 2000).”
An Improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations (2012, background): “The analysis of (1) is motivated by the study of vortex type configurations (see for example [4], [11], [26], [62] and [24], [33], [47], [54], [60], [61], [64]) in the Electroweak theory of Glashow-Salam-Weinberg [44], and in Self-Dual Chern-Simons theories [37], [41], [42].”