Mathematical Problems in Gravitation and CosmologyNo Access

COHOMOLOGICAL GAUGE THEORIES IN D > 4 WITH SPECIAL HOLONOMY Spin(7) AND G₂

BODO GEYER

Center of Theoretical Studies and Institute of Theoretical Physics, Leipzig University, Augustusplatz 10-11, D-04109 Leipzig, Germany

In memory of my former co-author Dietmar Mülsch who died March 2004 by a traffic accident.

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https://doi.org/10.1142/S0217751X05024821Cited by:1 (Source: Crossref)

Abstract

From Minkowskian 10D super Yang-Mills theory, by dimensional reduction and continuous Weyl-rotation, the 8D Euclidean, cohomological Spin(7)-invariant action is derived, by reduction to 7D the cohomological G₂-invariant action with global SU(2) symmetry obtains. Compatibility of chirality with generalized self-duality and octonionic algebra is shown. Using the chiral primary operator and the 8D analogue of the Pontryagin invariant a cohomological extension of has been constructed.

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References

D. Birmingham, M. Blau, M. Rakowski and G. Thompson, Phys. Rept. 209, 129 (1991); S. Cordes, G. Moore and S. Ramgoolam, hep-th/9411210 . Google Scholar
R. Dijkgraaf, E. Verline and H. Verlinde, Nucl. Phys. B352, 246 (1991). Google Scholar
E. Witten, Commun. Math. Phys. 117, 353 (1988). Crossref, Web of Science, ADS, Google Scholar
M. Blau and G. Thompson, Phys. Lett. B415, 242 (1997). ADS, Google Scholar
B. S. Acharya, M. O'Loughlin and B. Spence, Nucl. Phys. B503, 657 (1997). ADS, Google Scholar
L. Baulieu, H. Kanno and I. M. Singer, Commun. Math. Phys. 194, 149 (1998). Crossref, Web of Science, ADS, Google Scholar
L. Baulieu, A. Losev and N. Nekrasov, Nucl. Phys. B522, 82 (1998). ADS, Google Scholar
E. Corriganet al., Nucl. Phys. B214, 452 (1983). ADS, Google Scholar
G. Papadopoulos and P.K. Townsend, Phys. Lett. B357, 300 (1995); B. S. Acharya, hep-th/0011089; M. Atiyah, J. Maldacena and C. Vafa, J. Math. Phys. 42, 3209 (2001); M. Atiyah and E. Witten, Adv. Theor. Math. Phys. 6, 1 (2003) . Google Scholar
B. S. Acharyaet al., Nucl. Phys. B514, 583 (1998). ADS, Google Scholar
H. Nishino and S. Rajpoot, hep-th/0210132 . Google Scholar
D. Mülsch and B. Geyer, Int. J. Geom. Meth. Mod. Phys. 1, 185 (2004), hep-th/0310237. Link, Web of Science, Google Scholar
P. van Nieuwenhuizen and A. Waldron, Phys. Lett. B389, 29 (1996); A. Waldron, Phys. Lett. B433, 369 (1998) . Google Scholar
J. Yamron, Phys. Lett. B213, 325 (1988). ADS, Google Scholar
L. Baulieu and S. L. Shatashvili, JHEP 9903, 011 (1999). ADS, Google Scholar
D. Mülsch and B. Geyer, Nucl. Phys. B684, 351 (2004), hep-th/0310275. ADS, Google Scholar
D. Mülsch and B. Geyer, hep-th/0304096 . Google Scholar
L. Brink, J. H. Schwarz and J. Scherk, Nucl. Phys. B121, 41 (1993). Google Scholar
M. Berger, Bull. Soc. Math. France 83, 279 (1955). Google Scholar
E. Witten, Nucl. Phys. B460, 335 (1996). ADS, Google Scholar