Seiberg-Witten Equations on Pseudo-Riemannian Spin(c) Manifolds With Neutral Signature

DEĞİRMENCİ N., Karapazar S.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, vol.20, no.1, pp.73-88, 2012 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 1
  • Publication Date: 2012
  • Journal Name: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.73-88
  • Keywords: Neutral metric, Pseudo-Riemannian spine(c)-structure, Dirac operator, Seiberg-Witten equations
  • Anadolu University Affiliated: Yes

Abstract

Pseudo-Riemannian spin(c) manifolds were introduced by Ikemakhen in [7]. In the present work we consider pseudo-Riemannian 4-manifolds with neutral signature whose structure groups are SO+ (2, 2). We prove that such manifolds have pseudo-Riemannian spin(c) structure. We construct spinor bundle S and half-spinor bundles S+ and S- on these manifolds. For the first Seiberg-Witten equation we define Dirac operator on these bundles. Due to the neutral metric self-duality of a 2-form is meaningful and it enables us to write down second Seiberg-Witten equation. Lastly we write down the explicit forms of these equations on 4-dimensional flat space.