A Sharp Existence Theorem for Vortices in the Theory of Branes

2011/10/07 by Xiaosen Han, Han, Xiaosen
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Differential Equations and Numerical Methods #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1110.1423

Abstract

We investigate the BPS equations arising from the theory of multi-intersection of D-branes. By using the direct minimization method, we establish sharp existence and uniqueness theorems for multiple vortex solutions of the BPS equations over a doubly periodic domain and over the full plane, respectively. In particular, we obtain an explicit necessary and sufficient condition for the existence of a unique solution for the doubly periodic domain case.

Citations

• On the equivalence of the first and second order equations for gauge theories
• ArbitraryN-vortex solutions to the first order Ginzburg-Landau equations

Related

• Existence of Non-Abelian Vortices in the Aharony--Bergman--Jafferis--Maldacena Theory
• Intersecting Branes and Generalized Vortices
• BPS Vortices in Brane-Antibrane Effective Theory
• Solutions to the Master Equations Governing Fractional Vortices
• The Existence of Multi-vortices for a Generalized Self-dual Chern-Simons Model