By Hatcher A.

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Julia, and J. Scherk, Supergravity theory in 11 dimensions, Phys. Lett. B76 (1978), 409–412. 12. J. Dai, R. G. Leigh and J. Polchinski, New Connections Between String Theories, Mod. Phys. Lett. A 4, 2073 (1989). 13. P. Deligne and J. W. Morgan, Notes on Supersymmetry (following J. Bernstein), in Quantum Fields and Strings: A course for Mathematicians, eds. Deligne et al, pp. 41–97, 2 vols, AMS, Providence, 1999. 14. R. Dijkgraaf, Fields, strings and duality, in Les Houches 1995, Quantum symmetries, eds.

R. Douglas and A. Schwarz, Noncommutative Geometry and Matrix Theory: Compactiﬁcation on Tori, JHEP 9802 (1998) 003, [arXiv:hep-th/9711162]. 11. E. Cremmer, B. Julia, and J. Scherk, Supergravity theory in 11 dimensions, Phys. Lett. B76 (1978), 409–412. 12. J. Dai, R. G. Leigh and J. Polchinski, New Connections Between String Theories, Mod. Phys. Lett. A 4, 2073 (1989). 13. P. Deligne and J. W. Morgan, Notes on Supersymmetry (following J. Bernstein), in Quantum Fields and Strings: A course for Mathematicians, eds.

In fact, the local actions for supergravity theories in seven dimensions are actually determined by the number of massless vectors. So, in summary, we have shown that at generic points in M the low energy supergravity theories arising from M theory on K3 or the heterotic string on T3 are the same. At special points, some of the eigenvalues of the ﬂat connections will vanish. At these points the unbroken gauge group can get enhanced to a non-Abelian group. This is none other than the Higgs mechanism: the Higgs ﬁelds are just the Wilson lines.