Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-01-04
Physics
High Energy Physics
High Energy Physics - Theory
42 pages
Scientific paper
Using a two component $SL(2) $ isospinor formalism, we study the link between conifold $T^{\ast}\mathbb{S}^{3}$ and q-deformed non commutative holomorphic geometry in complex four dimensions. Then, thinking about conifold as a projective complex three dimension hypersurface embedded in non compact $WP^{5}(1,-1,1,-1,1,-1) $ space and using conifold local isometries, we study topological $SL(2) $ gauge theory on $T^{\ast}\mathbb{S}^{3}$ and its reductions to lower dimension sub-manifolds $T^{\ast}\mathbb{S}^{2}$, $T^{\ast}\mathbb{S}^{1}$ and their real slices. Projective symmetry is also used to build a supersymmetric QFT$%_{4}$ realization of these backgrounds. Extensions for higher dimensions with conifold like properties are explored. \bigskip \textbf{Key words}: Conifold, q-deformation, non commutative complex geometry, topological gauge theory. Nambu like background.
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