Abstract
In this article we consider T-dualization of the 3D closed bosonic string in the weakly curved background — constant metric and Kalb-Ramond field with one nonzero component, Bxy = Hz, where field strength H is infinitesimal. We use standard and generalized Buscher T-dualization procedure and make T-dualization starting from coordinate z, via y and finally along x coordinate. All three theories are nonlocal, because variable ΔV, defined as line integral, appears as an argument of background fields. After the first T-dualization we obtain commutative and associative theory, while after we T-dualize along y, we get, κ-Minkowski-like, noncommutative and associative theory. At the end of this T-dualization chain we come to the theory which is both noncommutative and nonassociative. The form of the final T-dual action does not depend on the order of T-dualization while noncommutativity and nonassociativity relations could be obtained from those in the x → y → z case by replacing H → −H.
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Nikolić, B., Obrić, D. Directly from H-flux to the family of three nonlocal R-flux theories. J. High Energ. Phys. 2019, 136 (2019). https://doi.org/10.1007/JHEP03(2019)136
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DOI: https://doi.org/10.1007/JHEP03(2019)136