Topological SL(2) Gauge Theory on Conifold

Abstract

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 $W{P}^5(1,-1,1,-1,1,-1)$ 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 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.

42 pages

References in corpus (2)

• N=1 and N=2 Geometry from Fluxes
• D-string fluid in conifold: I. Topological gauge model

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