Lectures on AKSZ Topological Field Theories for Physicists

Details Lectures on AKSZ Topological Field Theories for Physicists Lectures on AKSZ Topological Field Theories for Physicists

2012-04-17

arxiv.org/abs/1204.3714v1

Physics

High Energy Physics

High Energy Physics - Theory

66 pages

Scientific paper

This lecture provides an introductory review about topological field theories (TFT) called AKSZ type. The AKSZ construction is mathematical formulation to unify a large class of TFTs, inspired by the Batalin-Vilkovisky formalism of gauge theories. As an example, we start a simple topological field theory in two dimensions and explain ideas of the AKSZ construction. The construction in the example is generalized and led to a mathematical formulation of a general TFT, which is the AKSZ construction. Typical examples of AKSZ TFTs are listed including known and new TFTs. Mathematical objects for analysis of general gauge structures, a Lie algebroid and its variations are introduced. The quantization of the Poisson sigma model is explained as an example of quantizations.

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