Abelian Actions on Pseudo-real Riemann Surfaces

Non-abelian vortices on compact Riemann surfaces

We consider the vortex equations for a U(n) gauge field A coupled to a Higgs field φ with values on the n × n matrices. It is known that when these equations are defined on a compact Riemann surface Σ, their moduli space of solutions is closely related to a moduli space of τ -stable holomorphic n-pairs on that surface. Using this fact and a local factorization result for the matrix φ, we show t...

Abelian Gauge Theory on Riemann Surfaces

An Abelian gauge eld theory framed on a complex line bundle L over a compact Riemann surface M is developed which allows the coexistence, simultaneously in the same model, of magnetic vortices and antivortices represented by the N zeros and P poles of a section of L. The quantized minimum energy E is given in terms of the rst Chern class c 1 (L) and by a certain intersection number obtained fro...

Pseudo-real Riemann surfaces and chiral regular maps

A Riemann surface is called pseudo-real if it admits anticonformal automorphisms but no anticonformal involution. Pseudo-real Riemann surfaces appear in a natural way in the study of the moduli space MKg of Riemann surfaces considered as Klein surfaces. The moduli space Mg of Riemann surfaces of genus g is a two-fold branched covering of MKg , and the preimage of the branched locus consists of ...

Non - Abelian Vortices on Riemann Surfaces : an Integrable Case ∗

We consider U(n+1) Yang-Mills instantons on the space Σ×S2, where Σ is a compact Riemann surface of genus g. Using an SU(2)-equivariant dimensional reduction, we show that the U(n+1) instanton equations on Σ× S are equivalent to non-Abelian vortex equations on Σ. Solutions to these equations are given by pairs (A, φ), where A is a gauge potential of the group U(n) and φ is a Higgs field in the ...

Abelian Gauge Theory on Riemann Surfaces and New Topological Invariants