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 $Q$-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.

15 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018

References in corpus (7)

• Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries
• First order parent formulation for generic gauge field theories
• Parent formulations, frame-like Lagrangians, and generalized auxiliary fields
• Type-B Formal Higher Spin Gravity
• Parent formulation at the Lagrangian level
• Presymplectic structures and intrinsic Lagrangians
• Koszul-Tate resolutions as cofibrant replacements of algebras over differential operators

Cited by in corpus (13)

• On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
• Minimal models of field theories: Chiral Higher Spin Gravity
• A Worldline Theory for Supergravity
• Minimal model of Chiral Higher Spin Gravity
• Chiral Higher Spin Gravity and Convex Geometry
• Presymplectic structures and intrinsic Lagrangians for massive fields
• Presymplectic AKSZ formulation of Einstein gravity
• Higher Spin Gravities and Presymplectic AKSZ Models
• Minimal models of field theories: SDYM and SDGR
• A toy model for background independent string field theory
• Presymplectic gauge PDEs and Lagrangian BV formalism beyond jet-bundles
• Unfolded Formulation of 4d Yang-Mills Theory
• Supersymmetric Poisson and Poisson-supersymmetric sigma models