Special quantum field theories in eight-dimensions and other dimensions
Apr, 199734 pages
Published in:
- Commun.Math.Phys. 194 (1998) 149-175
e-Print:
- hep-th/9704167 [hep-th]
Report number:
- PAR-LPTHE-97-07
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Abstract:
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.Note:
- 36 pages, latex. References have been added together with a note Report-no: PAR--LPTHE 97/07
- gauge field theory: Yang-Mills
- gauge field theory: topological
- any-dimensional
- algebra: Becchi-Rouet-Stora
- differential forms
- supersymmetry
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