The asymptotic behavior of Chern-Simons Higgs model on a compact Riemann surface with boundary

2011 ◽  
Vol 28 (1) ◽  
pp. 145-170
Author(s):  
Meng Wang
Keyword(s):  
Asymptotic Behavior ◽  
Riemann Surface ◽  
Compact Riemann Surface ◽  
Higgs Model ◽  
Riemann Surface With Boundary ◽  
Chern Simons

THE SELF-DUAL CHERN–SIMONS HIGGS EQUATION ON A COMPACT RIEMANN SURFACE WITH BOUNDARY

2010 ◽  
Vol 21 (01) ◽  
pp. 67-76 ◽  
Author(s):  
MENG WANG
Keyword(s):  
Boundary Condition ◽  
Riemann Surface ◽  
Green Function ◽  
Neumann Boundary Condition ◽  
Compact Riemann Surface ◽  
Neumann Boundary ◽  
The Self ◽  
Almost Everywhere ◽  
Riemann Surface With Boundary ◽  
Chern Simons

We study the self-dual Chern–Simons Higgs equation on a compact Riemann surface with Neumann boundary condition. We show that the Chern–Simons Higgs equation with parameter λ > 0 has at least two solutions [Formula: see text] for λ sufficiently large, such that [Formula: see text] almost everywhere as λ → + ∞, and that [Formula: see text] almost everywhere as λ → ∞, where u0 is a (negative) Green function on M.

scholarly journals Embedded minimal surfaces of finite topology

2019 ◽  
Vol 2019 (753) ◽  
pp. 159-191 ◽  
Author(s):  
William H. Meeks III ◽  
Joaquín Pérez
Keyword(s):  
Asymptotic Behavior ◽  
Riemann Surface ◽  
Finite Number ◽  
Minimal Surface ◽  
Minimal Surfaces ◽  
Compact Riemann Surface ◽  
Finite Topology ◽  
Compact Boundary ◽  
Interior Points

AbstractIn this paper we prove that a complete, embedded minimal surface M in {\mathbb{R}^{3}} with finite topology and compact boundary (possibly empty) is conformally a compact Riemann surface {\overline{M}} with boundary punctured in a finite number of interior points and that M can be represented in terms of meromorphic data on its conformal completion {\overline{M}}. In particular, we demonstrate that M is a minimal surface of finite type and describe how this property permits a classification of the asymptotic behavior of M.

CLASSICAL AND CHERN-SIMONS VORTICES ON CURVED SPACE

1992 ◽  
Vol 07 (18) ◽  
pp. 4335-4352 ◽  
Author(s):  
PAOLO VALTANCOLI
Keyword(s):  
Asymptotic Behavior ◽  
Nonlinear Equation ◽  
Equations Of Motion ◽  
Higgs Model ◽  
Classical Dynamics ◽  
Critical Coupling ◽  
Vortex Equation ◽  
Curved Space ◽  
Vortex Model ◽  
Chern Simons

The classical dynamics of some vortex models coupled to gravity in the critical coupling is considered. We derive the set of Bogomol’nyi-type equations of motion for the Abelian Higgs model and for the Chern-Simons vortex model, coupled to gravity. In both cases we are able to reduce the dynamics to a single nonlinear equation which generalizes, on a curved space, the corresponding vortex equation on the plane. We finally compute in both cases the asymptotic behavior for a multivortex configuration from the N particle metric without and with spin, respectively.

scholarly journals Uniqueness of bubbling solutions of mean field equations with non-quantized singularities

2020 ◽  
pp. 2050038
Author(s):  
Lina Wu ◽  
Lei Zhang
Keyword(s):  
Riemann Surface ◽  
Compact Riemann Surface ◽  
Mean Field ◽  
Field Equations ◽  
Field Type ◽  
Dirac Mass ◽  
Mean Field Equations ◽  
The Mean ◽  
Chern Simons

For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions if some blowup points coincide with the singularities of the Dirac data. If the strength of the Dirac mass at each blowup point is not a multiple of [Formula: see text], we prove that bubbling solutions are unique. This paper extends previous results of Lin-Yan [C. S. Lin and S. S. Yan, On the mean field type bubbling solutions for Chern–Simons–Higgs equation, Adv. Math. 338 (2018) 1141–1188] and Bartolucci et al. [D. Bartolucci, A. Jevnikar, Y. Lee and W. Yang, Uniqueness of bubbling solutions of mean field equations, J. Math. Pures Appl. (9) 123 (2019) 78–126].

scholarly journals ON CANONICAL QUANTIZATION OF THE GAUGED WZW MODEL WITH PERMUTATION BRANES

2011 ◽  
Vol 26 (26) ◽  
pp. 4647-4660
Author(s):  
GOR SARKISSIAN
Keyword(s):  
Riemann Surface ◽  
Phase Space ◽  
Boundary Conditions ◽  
Canonical Quantization ◽  
Simons Theory ◽  
Gauge Fields ◽  
Time Line ◽  
Chern Simons ◽  
Special Case ◽  
Chern Simons Theory

In this paper we perform canonical quantization of the product of the gauged WZW models on a strip with boundary conditions specified by permutation branes. We show that the phase space of the N-fold product of the gauged WZW model G/H on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of the double Chern–Simons theory on a sphere with N holes times the time-line with G and H gauge fields both coupled to two Wilson lines. For the special case of the topological coset G/G we arrive at the conclusion that the phase space of the N-fold product of the topological coset G/G on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of Chern–Simons theory on a Riemann surface of the genus N-1 times the time-line with four Wilson lines.

Existence of radial solutions in the Chern–Simons–Higgs model with its N=2 SUSY extension

Nonlinearity ◽  
2021 ◽  
Vol 34 (6) ◽  
pp. 3907-3935
Author(s):  
Hsin-Yuan Huang ◽  
Hsien-Chung Kao
Keyword(s):  
Higgs Model ◽  
Radial Solutions ◽  
Chern Simons
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