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The eleven-dimensional supergravity equations on edge manifolds. (English) Zbl 1400.83055

Summary: We study the 11-dimensional supergravity equations which describe a low-energy approximation to string theories and are related to M-theory under the AdS/CFT correspondence. These equations take the form of a nonlinear differential system, on \(\mathbb B^7\times \mathbb S^4\) with the characteristic degeneracy at the boundary of an edge system, associated with the fibration with fiber \(\mathbb S^4.\) We compute the indicial roots of the linearized system from the Hodge decomposition of the 4-sphere following the work of Kantor, and then using the edge calculus [R. Mazzeo, Commun. Partial Differ. Equations 16, No. 10, 1615–1664 (1991; Zbl 0745.58045)] and scattering theory, we prove that the moduli space of solutions, near the Freund-Rubin states, is parametrized by three pairs of data on the bounding 6-sphere.

MSC:

83E50 Supergravity
83E30 String and superstring theories in gravitational theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
58J05 Elliptic equations on manifolds, general theory

Citations:

Zbl 0745.58045
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References:

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