Gauge PDE and AKSZ-type Sigma Models
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 -bundles. In particular, we demonstrate that any gauge PDE can be embedded into a super-jet bundle of the -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.
Keywords
Cite
@article{arxiv.1903.02820,
title = {Gauge PDE and AKSZ-type Sigma Models},
author = {Maxim Grigoriev and Alexei Kotov},
journal= {arXiv preprint arXiv:1903.02820},
year = {2019}
}
Comments
15 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018