Seiberg-Witten Monopole Equations And Riemann Surfaces

Details Seiberg-Witten Monopole Equations And Riemann Surfaces Seiberg-Witten Monopole Equations And Riemann Surfaces

1997-03-07

arxiv.org/abs/hep-th/9703057v1

Nucl.Phys. B503 (1997) 675-687

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 23 pages.

Scientific paper

10.1016/S0550-3213(97)00457-4

The twice-dimensionally reduced Seiberg-Witten monopole equations admit solutions depending on two real parameters (b,c) and an arbitrary analytic function f(z) determining a solution of Liouville's equation. The U(1) and manifold curvature 2-forms F and R^1_2 are invariant under fractional SL(2,R) transformations of f(z). When b=1/2 and c=0 and f(z) is the Fuchsian function uniformizing an algebraic function whose Riemann surface has genus p \geq 2 , the solutions, now SL(2,R) invariant, are the same surfaces accompanied by a U(1) bundle of c_1=\pm (p-1) and a 1-component constant spinor.

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