Beta, Dipole and Noncommutative Deformations of M-theory Backgrounds with One or More Parameters

Understand

We construct new M-theory solutions starting from those that contain 5 U(1) isometries.

• We do this by reducing along one of the 5-torus directions, then T-dualizing via the action of an O(4,4) matrix and lifting back to 11-dimensions.
• The particular T-duality transformation is a sequence of O(2,2) transformations embedded in O(4,4), where the action of each O(2,2) gives a Lunin-Maldacena deformation in 10-dimensions.
• We find general formulas for the metric and 4-form field of single and multiparameter deformed solutions, when the 4-form of the initial 11-dimensional background has at most one leg along the 5-torus.