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

TL;DR

This paper develops a systematic method to generate new M-theory solutions with multiple deformation parameters by applying T-duality transformations, extending known deformations like beta, dipole, and noncommutative types.

Contribution

It introduces general formulas for deformed M-theory backgrounds with multiple parameters, based on O(4,4) transformations, and applies these to various AdS backgrounds.

Findings

Derived explicit formulas for deformed metrics and 4-form fields.

Constructed multi-parameter deformed solutions from original backgrounds.

Extended deformation techniques to cases with fewer U(1) isometries.

Abstract

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. All the deformation terms in the new solutions are given in terms of subdeterminants of a 5x5 matrix, which represents the metric on the 5-torus. We apply these results to several M-theory backgrounds of the type AdS_r x X^{11-r}. By appropriate choices of the T-duality and reduction directions we obtain analogues of beta, dipole and noncommutative deformations. We also provide formulas for backgrounds with only 3 or 4 U(1) isometries and study a case, for which our assumption for the 4-form field is violated.