Bootstrapping non-commutative gauge theories from L∞ algebras

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DOI Доступ к ресурсу на сайте издателя			10.1007/JHEP05(2018)097

Title: Bootstrapping non-commutative gauge theories from L∞ algebras
Creator: Brunner, Ilka
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Kupriyanov, Vladislav G.
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Lüst, Dieter
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Blumenhagen, Ralph
Date: 2018
DOI: 10.1007/JHEP05(2018)097
Description: Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L$_infty$ algebra, that governs not only the action of the symmetries but also the dynamics of the theory. Our approach is well motivated from string theory. We recall that such field theories arise in the context of branes in WZW models and briefly comment on its appearance for integrable deformations of AdS$_5$ sigma models. For the SU(2) WZW model, we show that the earlier proposed matrix valued gauge theory on the fuzzy 2-sphere can be bootstrapped via an L$_infty$ algebra. We then apply this approach to the construction of non-commutative Chern-Simons and Yang-Mills theories on flat and curved backgrounds with non-constant NC-structure. More concretely, up to the second order, we demonstrate how derivative and curvature corrections to the equations of motion can be bootstrapped in an algebraic way from the L$_infty$ algebra. The appearance of a non-trivial A$_infty$ algebra is discussed, as well.

Created: 01-10-2020

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Физический факультет Bootstrapping non-commutative gauge theories from L∞ algebras