Matrix theory compactifications on twisted tori

Abstract

We study compactifications of Matrix theory on twisted tori and non-commutative 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 non-commutative torus with non-constant non-commutativity and an underlying non-associative structure on its phase space. Next we turn our attention to 3- and 6-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 non-commutative 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.

1+31 pages, v2: some comments and clarifications added, accepted for publication in Physical Review D

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Cited by in corpus (7)

• Double Field Theory: A Pedagogical Review
• Quantum field theory on toroidal topology: algebraic structure and applications
• Matrix theory origins of non-geometric fluxes
• Dirac structures on nilmanifolds and coexistence of fluxes
• Brane compactifications and 4-dimensional geometry in the IKKT model
• Phase space quantization, noncommutativity and the gravitational field
• Fluxes, Twisted tori, Monodromy and $U(1)$ Supermembranes