Acharya, B. S.; O’Loughlin, M.; Spence, B. Higher-dimensional analogues of Donaldson-Witten theory. (English) Zbl 0938.81035 Nucl. Phys., B 503, No. 3, 657-674 (1997). Summary: We present a Donaldson-Witten-type field theory in eight dimensions on manifolds with Spin(7) holonomy. We prove that the stress tensor is BRST exact for metric variations preserving the holonomy and we give the invariants for this class of variations. In six and seven dimensions we propose similar theories on Calabi-Yau threefolds and manifolds of \(G_2\) holonomy, respectively. We point out that these theories arise by considering supersymmetric Yang-Mills theory defined on such manifolds. The theories are invariant under metric variations preserving the holonomy structure without the need for twisting. This statement is a higher-dimensional analogue of the fact that Donaldson-Witten field theory on hyper-Kähler 4-manifolds is topological without twisting. Higher-dimensional analogues of Floer cohomology are briefly outlined. All of these theories arise naturally within the context of string theory. Cited in 28 Documents MSC: 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 58D29 Moduli problems for topological structures 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 57R57 Applications of global analysis to structures on manifolds 81T13 Yang-Mills and other gauge theories in quantum field theory Keywords:manifolds; BRST exact stress tensor; metric variations; holonomy preservation; Calabi Yau threefolds; supersymmetric Yang Mills theory; hyper Kähler 4 manifolds; topological field theory; higher dimensional Floer cohomology; instanton equations PDFBibTeX XMLCite \textit{B. S. Acharya} et al., Nucl. Phys., B 503, No. 3, 657--674 (1997; Zbl 0938.81035) Full Text: DOI arXiv References: [1] Witten, E., Commun. Math. Phys., 117, 353 (1988) [2] Corrigan, E.; Devchand, C.; Fairlie, D., J. Nuyts, Nucl. Phys. B, 214, 452 (1983) [3] Acharya, B. S.; O’Loughlin, M., Phys. Rev. D, 55, R4521 (1997) [4] Joyce, D. D., Inv. Math., 123, 507 (1996) [5] Gibbons, G.; Page, D.; Pope, C., Commun. Math. Phys., 127, 529 (1990) [6] Wang, M. Y., Indiana Univ. Math. J., 40, 815 (1991) [7] Vafa, C.; Witten, E., Nucl. Phys. B, 431, 3 (1994) [8] Berger, M., Bull. Soc. Math. France, 83, 279 (1955) [9] Dündarer, R.; Gürsey, F.; Tze, C.-H., J. Math. Phys., 25, 1496 (1984) [10] Bonan, E., C.R. Acad. Sci. Paris, 262, 127 (1966) [11] Bryant, R.; Salamon, S., Duke Math. J., 58, 829 (1989) [12] Witten, E., Int. J. Mod. Phys. A, 6, 2725 (1991) [13] Birmingham, D.; Blau, M.; Rakowski, M.; Thompson, G., Phys. Rep., 209, 129 (1991) [14] Candelas, P.; Horowitz, G.; Strominger, A.; Witten, E., Nucl. Phys. B, 258, 46 (1985) [15] Papadopoulos, G.; Townsend, P., Phys. Lett. B, 357, 300 (1995) [16] Acharya, B. S., Nucl. Phys. B, 492, 591 (1997) [17] M. Blau and G. Thompson, private communication.; M. Blau and G. Thompson, private communication. [18] Witten, E., Nucl. Phys. B, 460, 335 (1996) [19] Bershadsky, M.; Sadov, V.; Vafa, C., Nucl. Phys. B, 463, 420 (1996) [20] Blau, M.; Thompson, G., Nucl. Phys. B, 492, 545 (1997) [21] Harvey, R.; Lawson, H. B., Acta. Math., 148, 47 (1982) [22] L. Baulieu, I. Kanno and I. Singer, hep-th/9704167.; L. Baulieu, I. Kanno and I. Singer, hep-th/9704167. [23] S.K. Donaldson and R.E Thomas, Oxford preprint.; S.K. Donaldson and R.E Thomas, Oxford preprint. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.