Special Quantum Field Theoriesin Eight and Other Dimensions
Abstract
We build nearly topological quantum field theories in various dimensions. We give special attention to the case of eight dimensions for which we first consider theories depending only on YangMills 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 CalabiYau 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 Ftheories. Relations to the eight dimensional supersymmetric YangMills theory are presented. Then, by dimensional reduction, we obtain other theories, in particular a four dimensional one whose gauge conditions are identical to the nonabelian SeibergWitten equations. The latter are thus related to pure YangMills selfduality equations in 8 dimensions as well as to the N=1, D=10 super YangMills theory. We also exhibit a theory that couples 3form gauge fields to the second Chern class in eight dimensions, and interesting theories in other dimensions.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1998
 DOI:
 10.1007/s002200050353
 arXiv:
 arXiv:hepth/9704167
 Bibcode:
 1998CMaPh.194..149B
 Keywords:

 High Energy Physics  Theory
 EPrint:
 36 pages, latex. References have been added together with a note