Gauge Theory And Integrability, I

Integrability in N=2 Gauge Theory: A Proof

The holomorphic prepotential of ultraviolet finite N=2 supersymmetric gauge theories is obtained by a partial twisting of N=1 gauge theory in six dimensions, compactified on IR × T2. We show that Ward identities for the conserved chiral R-symmetry in these theories generate a set of constraints on the correlation functions of chiral ring operators. These correlators depend only on the coordinat...

Higher - Loop Integrability in N = 4 Gauge Theory

The dilatation operator measures scaling dimensions of local operator in a conformal field theory. Algebraic methods of constructing the dilatation operator in four-dimensional N = 4 gauge theory are reviewed. These led to the discovery of novel integrable spin chain models in the planar limit. Making use of Bethe ansätze a superficial discrepancy in the AdS/CFT correspondence was found, we dis...

The Integrability Criterion in SU(2) Chern-Simons Gauge Theory

We prove that the multiplicity spaces appearing in Chern-Simons theory, as defined by Segal, vanish unless they are associated to integrable representations. This and other links with conformal field theory are examined.

Gauge theory and calibrated geometry , I

Higher gauge theory I: 2-Bundles

I categorify the definition of fibre bundle, replacing smooth manifolds with differentiable categories, Lie groups with coherent Lie 2-groups, and bundles with a suitable notion of 2-bundle. To link this with previous work, I show that certain 2-categories of principal 2-bundles are equivalent to certain 2-categories of (nonabelian) gerbes. This relationship can be (and has been) extended to co...