A NOTE ON ANTI SELF DUAL SU(3) GAUGE THEORY OVER A SIX-DIMENSIONAL MANIFOLD

Kilicman A., Ozel C., Sener I., Uddin S., Zainuddin H.

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, vol.70, no.4, pp.477-488, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 70 Issue: 4
  • Publication Date: 2017
  • Journal Name: COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.477-488
  • Keywords: Six-dimensional manifold, SU(3)Yang Mills theory, Phi-duality, topological bound, Phi-topological charge, EQUATIONS, DIMENSIONS
  • Dokuz Eylül University Affiliated: Yes

Abstract

The bundle of the 2-forms over a 6-dimensional base manifold decomposes to three subbundles such that Lambda(2)(R-6) Lambda(2)(1) 619 Lambda(2)(6) circle plus Lambda(2)(8) with dimensions 1, 6 and 8, respectively. A duality notion for the 2-forms called Phi-duality is given by equation eta = lambda(*Phi) (eta boolean AND Phi) and an anti self dual SU(3) Yang-Mills theory is studied on the subbundle Lambda(2)(6). The curvature 2-form in such a theory is closed and its components are constants. The integral of the total action is bounded by the second Chern class of the bundle such that integral(M) L-m (F) >= -87 pi(2) integral(M) ch(2) boolean AND Phi This bound created a stability case for the total action integral. This stability case is satisfied by the coupling constant. Thus the total pseudo energy becomes proportional to that of Yang-Mills action integral, and at the same time to the Phi-topological charge. Also one sees that, when the base manifold is M = S-4 subset of R-6, this stability case serves the quantization condition like in the sense of Dirac. At the origin and infinity of the four dimensional sphere S-4, the connection becomes flat.