Resolution of Chern--Simons--Higgs Vortex Equations
arXiv:1503.08330 · doi:10.1007/s00220-016-2571-5
Abstract
It is well known that the presence of multiple constraints of non-Abelian relativisitic Chern--Simons--Higgs vortex equations makes it difficult to develop an existence theory when the underlying Cartan matrix of the equations is that of a general simple Lie algebra and the strongest result in the literature so far is when the Cartan subalgebra is of dimension 2. In this paper we overcome this difficulty by implicitly resolving the multiple constraints using a degree-theorem argument, utilizing a key positivity property of the inverse of the Cartan matrix deduced in an earlier work of Lusztig and Tits, which enables a process that converts the equality constraints to inequality constraints in the variational formalism. Thus this work establishes a general existence theorem which settles a long-standing open problem in the field regarding the general solvability of the equations.
28 pages
References in corpus (9)
- N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
- Gauge Symmetry and Supersymmetry of Multiple M2-Branes
- Algebraic structures on parallel M2-branes
- Modeling Multiple M2's
- Splitting Instability of a Multiply Charged Vortex in a Bose-Einstein Condensate
- The Power of the Higgs Mechanism: Higher-Derivative BLG Theories
- Vortex-type Half-BPS Solitons in ABJM Theory
- Proof of the Julia-Zee Theorem
- Relativistic Chern--Simons--Higgs Vortex Equations