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Classical and quantum aspects of field theory on non-geometric backgrounds


Non-commutativity is quite natural in string theory. For open strings it appears due to the presence of non-vanishing background two-form in the world volume of Dirichlet brane, while in closed string theory the flux compactifications with non-vanishing three-form also lead to non-commutativity. Except for some very specific cases, like the constant $B$-field in open string theory, the string coordinates are not only non-commutative, but also non-associative. It manifests the non-geometric nature of the consistent string vacua. The aim of this project is to study the consistency of the mathematical framework necessary to work with non-associativity, as well as the investigation of the possible physical consequences of the non-geometric backgrounds on the level of field theory and quantum mechanics. (AU)

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Scientific publications (6)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
KUPRIYANOV, VLADISLAV G.; SZABO, RICHARD J.. Symplectic realization of electric charge in fields of monopole distributions. Physical Review D, v. 98, n. 4, . (16/04341-5)
KUPRIYANOV, VLADISLAV G.; SZABO, RICHARD J.. G(2)-structures and quantization of non-geometric M-theory backgrounds. Journal of High Energy Physics, n. 2, . (16/04341-5)
KUPRIYANOV, V. G.. Weak associativity and deformation quantization. Nuclear Physics B, v. 910, p. 240-258, . (16/04341-5, 14/03578-6)
BARNES, GWENDOLYN E.; SCHENKEL, ALEXANDER; SZABO, RICHARD J.. Mapping spaces and automorphism groups of toric noncommutative spaces. LETTERS IN MATHEMATICAL PHYSICS, v. 107, n. 9, p. 1591-1628, . (16/04341-5)
BUNK, SEVERIN; SAEMANN, CHRISTIAN; SZABO, RICHARD J.. The 2-Hilbert space of a prequantum bundle gerbe. REVIEWS IN MATHEMATICAL PHYSICS, v. 30, n. 1, . (16/04341-5)
HEKMATI, PEDRAM; MURRAY, MICHAEL K.; SZABO, RICHARD J.; VOZZO, RAYMOND F.. Real bundle gerbes, orientifolds and twisted KR-homology. Advances in Theoretical and Mathematical Physics, v. 23, n. 8, p. 2093-2159, . (16/04341-5)

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