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• W1777579202 abstract "In this contribution we review some of the interplay between sigma models in theoretical physics and novel geometrical structures such as Lie (n-)algebroids. The first part of the article contains the mathematical background, the definition of various algebroids as well as of Dirac structures, a joint generalization of Poisson, presymplectic, but also complex structures. Proofs are given in detail. The second part deals with sigma models. Topological ones, in particular the AKSZ and the Dirac sigma models, as generalizations of the Poisson sigma models to higher dimensions and to Dirac structures, respectively, but also physical ones, that reduce to standard Yang Mills theories for the “flat” choice of a Lie algebra: Lie algebroid Yang–Mills theories and possible action functionals for nonabelian gerbes and general higher gauge theories. Characteristic classes associated to Dirac structures and to higher principal bundels are also mentioned." @default.
• W1777579202 created "2016-06-24" @default.
• W1777579202 creator A5026655393 @default.
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• W1777579202 date "2010-06-10" @default.
• W1777579202 modified "2023-09-26" @default.
• W1777579202 title "Generalizing geometry – algebroids and sigma models" @default.
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• W1777579202 doi "https://doi.org/10.4171/079-1/7" @default.
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