Generalizing Geometry - Algebroids and Sigma Models
作者： T. Strobl , A. Kotov
DOI:
关键词: Gauge theory 、 Yang–Mills existence and mass gap 、 Theoretical physics 、 Lie algebra 、 Sigma 、 Generalization 、 Dirac (software) 、 Physics 、 Lie algebroid 、 Characteristic class
摘要: 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 article contains mathematical background, definition various algebroids well Dirac structures, a joint generalization Poisson, presymplectic, but also complex structures. Proofs are given detail. second deals with models. Topological ones, particular AKSZ models, generalizations Poisson to higher dimensions respectively, physical that reduce standard Yang Mills theories for "flat" choice algebra: algebroid possible action functionals nonabelian gerbes general gauge theories. Characteristic classes associated principal bundles mentioned.
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