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arXiv · 1903.02820

Gauge PDE and AKSZ-type Sigma Models

Maxim Grigoriev·Alexei Kotov
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Abstract

A gauge PDE is a natural notion which arises by abstracting what physicists call a local gauge field theory defined in terms of BV-BRST differential (not necessarily Lagrangian). We study supergeometry of gauge PDEs paying particular attention to globally well-defined definitions and equivalences of such objects. We demonstrate that a natural geometrical language to work with gauge PDEs is that of $Q$-bundles. In particular, we demonstrate that any gauge PDE can be embedded into a super-jet bundle of the $Q$-bundle. This gives a globally well-defined version of the so-called parent formulation. In the case of reparameterization-invariant systems, the parent formulation takes the form of an AKSZ-type sigma model with an infinite-dimensional target space.

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Maxim Grigoriev, Alexei Kotov. 2019-04-22. Gauge PDE and AKSZ-type Sigma Models. https://doi.org/10.1002/prop.201910007

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