Special Quantum Field Theories In Eight And Other Dimensions

Details Special Quantum Field Theories In Eight And Other Dimensions Special Quantum Field Theories In Eight And Other Dimensions

1997-04-24

arxiv.org/abs/hep-th/9704167v2

Commun.Math.Phys. 194 (1998) 149-175

Physics

High Energy Physics

High Energy Physics - Theory

36 pages, latex. References have been added together with a note

Scientific paper

10.1007/s002200050353

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.

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