1997/04/30 by Laurent Baulieu, L. Baulieu, Hiroaki Kanno +2 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Field (mathematics) #Gauge theory #Holomorphic function #Holonomy #Homotopy and Cohomology in Algebraic Topology #Manifold (fluid mechanics) #Noncommutative and Quantum Gravity Theories #Observable #Quantum #Quantum field theory #Topological quantum field theory #hep-th
paper · pdf · doi:10.1007/s002200050353
published as Commun.Math.Phys. 194 (1998) 149-175 · 36 pages, latex. References have been added together with a note
arxiv created 1997/07/30 · openalex publication_date 1998/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We build nearly topological quantum field theories in various dimensions. We give special attention to the case of 8 dimensions for which we first consider theories depending only on Yang-Mills fields. Two classes of gauge functions exist which correspond to the choices of two different holonomy groups in SO(8), namely SU(4) and Spin(7). The choice of SU(4) gives a quantum field theory for a Calabi-Yau fourfold. The expectation values for the observables are formally holomorphic Donaldson invariants. The choice of Spin(7) defines another eight dimensional theory for a Joyce manifold which could be of relevance in M- and F-theories. Relations to the eight dimensional supersymmetric Yang-Mills theory are presented. Then, by dimensional reduction, we obtain other theories, in particular a four dimensional one whose gauge conditions are identical to the non-abelian Seiberg-Witten equations. The latter are thus related to pure Yang-Mills self-duality equations in 8 dimensions as well as to the N=1, D=10 super Yang-Mills theory. We also exhibit a theory that couples 3-form gauge fields to the second Chern class in eight dimensions, and interesting theories in other dimensions.