Higgs Bundles and Four Manifolds

Abstract

It is known that the Seiberg-Witten invariants, derived from supersymmetric Yang-Mill theories in four-dimensions, do not distinguish smooth structure of certain non-simply-connected four manifolds. We propose generalizations of Donaldson-Witten and Vafa-Witten theories on a Kähler manifold based on Higgs Bundles. We showed, in particular, that the partition function of our generalized Vafa-Witten theory can be written as the sum of contributions our generalized Donaldson-Witten invariants and generalized Seiberg-Witten invariants. The resulting generalized Seiberg-Witten invariants might have, conjecturally, information on smooth structure beyond the original Seiberg-Witten invariants for non-simply-connected case.

29 pages, LaTeX2e

References in corpus (11)

• Issues in Topological Gauge Theory
• Extending Mirror Conjecture to Calabi-Yau with Bundles
• The Donaldson-Witten function for gauge groups of rank larger than one
• Donaldson invariants for nonsimply connected manifolds
• N=4 Supersymmetric Yang-Mills Theory on a Kaehler Surface
• Integrating over the Coulomb branch in N=2 gauge theory
• Mass Perturbations in Twisted N=4 Supersymmetric Gauge Theories
• Duality in twisted N=4 supersymmetric gauge theories in four dimensions
• Monads and D-instantons
• Sigma Models for Bundles on Calabi-Yau: A Proposal for Matrix String Compactifications
• Cohomological Field Theories with Kähler Structure