2014/01/22 by Yiwen Pan, Pan, Yiwen
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1401.5733
openalex publication_date 2014/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the localization of 5-dimensional N = 1 super-Yang-Mills, contact-instantons arise as non-perturbative contributions. In this note, we revisit such configurations and discuss their generalizations. We propose for contact-instantons a cohomological theory whose BRST observables are invariants of the background contact geometry. To make the formalism more concrete, we study the moduli problem of contact- instanton, and we find that it is closely related to the eqiuivariant index of a canonical Dirac-Kohn operator associated to the geometry. An integral formula is given when the geometry is K-contact. We also discuss the relation to 5d N = 1 super-Yang- Mills, and by studying a contact-instanton solution canonical to the background geometry, we discuss a possible connection between N = 1 theory and contact homology. We also uplift the 5d theory a 6d cohomological theory which localizes to Donaldson-Uhlenbeck-Yau instantons when placed on special geometry.