engleski

Matrix theory compactifications on twisted tori

We study compactifications of Matrix theory on twisted tori and noncommutative versions of them. As a first step, we review the construction of multidimensional twisted tori realized as nilmanifolds based on certain nilpotent Lie algebras. Subsequently, matrix compactifications on tori are revisited, and the previously known results are supplemented with a background of a noncommutative torus with nonconstant noncommutativity and an underlying nonassociative structure on its phase space. Next, we turn our attention to three- and six-dimensional twisted tori, and we describe consistent backgrounds of Matrix theory on them by stating and solving the conditions which describe the corresponding compactification. Both commutative and noncommutative solutions are found in all cases. Finally, we comment on the correspondence among the obtained solutions and flux compactifications of 11-dimensional supergravity, as well as on relations among themselves, such as Seiberg-Witten maps and T-duality.

matrix theory ; compactification ; twisted torus

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