Dimensional Reduction of Dual Topological Theories

Olsen, Kasper

doi:10.1142/s0217732396001764

Cited by 7 publications

(2 citation statements)

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“…These topological features are found to be invariant under a wide class of transformations on the metric and other fields. This is perhaps a reflection of the connection, pointed out by Olsen [5], between twice-dimensionally reduced SWME and certain 2d topological field theories [6].…”

Section: Introductionmentioning

confidence: 77%

Seiberg-Witten monopole equations and Riemann surfaces

Saçliog̃lu

Nergiz

1997

Nuclear Physics B

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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, IR) 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 ≥ 2 , the solutions, now SL(2, IR) invariant, are the same surfaces accompanied by a U (1) bundle of c 1 = ±(p − 1) and a 1-component constant spinor.

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Section: Introductionmentioning

confidence: 77%

Seiberg-Witten monopole equations and Riemann surfaces

Saçliog̃lu

Nergiz

1997

Nuclear Physics B

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“…A reduction which gives the "vortex" equations have been studied extensively e.g. Taubes [30], Bradlow, Garcia-Prada [5], Olsen [26], Nergiz and Saclioglu [23], [24] and others. This reduction does not have a Higgs field.…”

Section: Introductionmentioning

confidence: 99%

Symplectic and hyperkähler structures in a dimensional reduction of the Seiberg-Witten equations with a Higgs field

Dey

2002

Reports on Mathematical Physics

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Abstract. In this paper we show that the dimensionally reduced SeibergWitten equations lead to a Higgs field and study the resulting moduli spaces. The moduli space arising out of a subset of the equations, shown to be nonempty for a compact Riemann surface of genus g ≥ 1, gives rise to a family of moduli spaces carrying a hyperkähler structure. For the full set of equations the corresponding moduli space does not have the aforementioned hyperkähler structure but has a natural symplectic structure. For the case of the torus, g = 1, we show that the full set of equations has a solution, different from the "vortex solutions".

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