SEIBERG-WITTEN LIKE EQUATIONS ON 8-MANIFOLDS WITH STRUCTURE GROUP SPIN(7)

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ÖZDEMİR N., Dedirmenci N.

JOURNAL OF DYNAMICAL SYSTEMS AND GEOMETRIC THEORIES, vol.7, no.1, pp.21-39, 2009 (ESCI)

• Publication Type: Article / Article
• Volume: 7 Issue: 1
• Publication Date: 2009
• Doi Number: 10.1080/1726037x.2009.10698560
• Journal Name: JOURNAL OF DYNAMICAL SYSTEMS AND GEOMETRIC THEORIES
• Journal Indexes: Emerging Sources Citation Index (ESCI)
• Page Numbers: pp.21-39
• Keywords: Seiberg-witten equations, Spinor, Spin(7)-structure, FIELDS
• Anadolu University Affiliated: Yes

Abstract

Seiberg-Witten monopole equations are defined on 4-manifolds and solution space of this equations yields differential topological invariants. In this work we consider 8-dimensional Riemannian manifolds with structure group Spin(7). Such manifolds have a distinguished 4-form. By using this 4-form we define self-dual 2-form in dimension eight which is consistent with the well known self-duality notion in 8-dimension given by CDFN (see [5]). We then express Seiberg-Witten like equations in 8-dimension as analogues of Seiberg-witten equations in 4-dimension.