Compactifying Solutions of D = 11 Supergravity

Abstract

We construct infinite families of Lifshitz solutions of D = 10 and D = 11 supergravity with dynamical exponent z = 2. The new solutions are based on five-and seven-dimensional Einstein manifolds and are dual to field theories with Lifshitz scaling in 1+2 and 1+1 spacetime dimensions, respectively. When the Einstein spaces are Sasaki-Einstein, the solutions are supersymmetric.

Constrained supermanifolds for AdS M-theory backgrounds

“…As we already mentioned in the introduction there exist several compact manifolds of weak G 2 holonomy. In particular all the coset manifolds G/H of weak G 2 holonomy were classified and studied in the Kaluza Klein supergravity age [31,26,32,33,34,35,36,29,37,38] and they were extensively reconsidered in the context of the AdS/CFT correspondence [39,40,41,42,43].…”

“…We recall that all our indices are flat since we systematically use differential forms. Furthermore we have tried to incorporate consistently into our framework the index conventions adopted in the series of papers ( [29,44,23,26,32,33,34]), dating back to the eighties and relative to the classification and construction of Freund Rubin compactifications and readopted in the series of papers ( [40,41,42,43,49]) relative to the reinterpretation of such solutions into the context of the AdS/CF T correspondence. 5.…”

“…5. Slightly modifying the general conventions of papers [29,29,44,26,32,34], the underlined capital latin indices from the beginning of the alphabet A, B, C, . .…”

Twisted tori and fluxes: A no go theorem for Lie groups of weak holonomy

“…As we already mentioned in the introduction there exist several compact manifolds of weak G 2 holonomy. In particular all the coset manifolds S/R of weak G 2 holonomy were classified and studied in the Kaluza Klein supergravity age [57,58,59,60,61] and they were extensively reconsidered in the context of the AdS/CFT correspondence [66,67,68,69,70]. No one so far formulated and answered the question whether there exist 7-parameter Lie group manifolds G of weak G 2 holonomy.…”

“…See[53] for a comprehensive review and the basic original literature for the various families of S/R spaces namely[54,55,56] for S 7 ,[57] for the squashed S 7 ,[58] for the M pqr spaces,[59] for Q pqr spaces,[60] for the N pqr spaces and[61] for the exhaustive classification of the remaining ones.…”