Gauge theory, calibrated geometry and harmonic spinors

Gauge theory , calibrated geometry and harmonic spinors Andriy

We establish connections between different gauge-theoretical problems in high and low dimensions. In particular we show that higher dimensional asd equations on total spaces of spinor bundles over low dimensional manifolds can be interpreted as Taubes-Pidstrygach’s generalisation of Seiberg-Witten equations. By collapsing each fibre of the spinor bundle to a point, we relate solutions of Taubes...

Spacetime Geometry with Geometric Calculus

Geometric Calculus is developed for curved-space treatments of General Relativity and comparison with the flat-space gauge theory approach by Lasenby, Doran and Gull. Einstein’s Principle of Equivalence is generalized to a gauge principle that provides the foundation for a new formulation of General Relativity as a Gauge Theory of Gravity on a curved spacetime manifold. Geometric Calculus provi...

Gauge theory and calibrated geometry , I

Conformal properties of harmonic spinors and lightlike geodesics in signature (1, 1)

We are studying the harmonic and twistor equation on Lorentzian surfaces, that is a two dimensional orientable manifold with a metric of signature (1, 1). We will investigate the properties of the solutions of these equations and try to relate the conformal invariant dimension of the space of harmonic and twistor spinors to the natural conformal invariants given by the Lorentzian metric. We wil...

Harmonic Superspaces from Superstrings

We derive harmonic superspaces for N = 2, 3, 4 SYM theory in four dimensions from superstring theory. The pure spinors in ten dimensions are dimensionally reduced and yield the harmonic coordinates. Two anticommuting BRST charges implement Grassmann analyticity and harmonic analyticity. The string field theory action produces the action and field equations for N=3 SYM theory in harmonic supersp...