Presymplectic BV-AKSZ and constrained DGCAs
Abstract
The AKSZ construction encodes the Batalin-Vilkovisky formulation of a topological field theory in terms of finite-dimensional geometric data. There are at least two ways to extend this approach to nontopological gauge theories. The first, due to Costello, replaces the spacetime exterior algebra with a more general DGCA that is not freely generated. The second replaces the symplectic structure with a degenerate presymplectic structure, which may also be non-regular. In this work, we show that both approaches are special cases of a more general algebraic AKSZ construction, in which the underlying algebras are allowed to be constrained and the presymplectic structure may be degenerate and non-regular. Within this framework, we explicitly relate Costello's formulation of the Chalmers-Siegel model to the presymplectic formulation, the latter admitting a first-principles derivation. We also construct Costello-like formulations of higher-form analogues of the Chalmers-Siegel model and of self-dual higher-spin gauge theories of Yang-Mills type, obtaining in the latter case a remarkably concise description. In so doing we propose a simple algebraic construction for the corresponding source space DGCAs underlying these examples.
Related
- Topological deformations of local gauge theories: a presymplectic BV-AKSZ approach
- Reduction of symmetric time-dependent Hamiltonian systems I: presymplectic principal ℝ-bundles
- Gauged AKSZ sigma models
- AKSZ Construction for Shifted Contact Structures
- Relative Logarithmic AKSZ Descent on Joyce Generalized Corners
BibTeX
@misc{grigoriev2026presymplectic,
title = {{Presymplectic BV-AKSZ and constrained DGCAs}},
author = {Maxim Grigoriev and Alexander Mamekin and Dmitry Rudinsky},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10859},
eprint = {2609.10859},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10859},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Presymplectic BV-AKSZ and constrained DGCAs
AU - Maxim Grigoriev
AU - Alexander Mamekin
AU - Dmitry Rudinsky
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10859
UR - https://arxiv.org/abs/2609.10859
AB - The AKSZ construction encodes the Batalin-Vilkovisky formulation of a topological field theory in terms of finite-dimensional geometric data. There are at least two ways to extend this approach to nontopological gauge theories. The first, due to Costello, replaces the spacetime exterior algebra with a more general DGCA that is not freely generated. The second replaces the symplectic structure with a degenerate presymplectic structure, which may also be non-regular. In this work, we show that both approaches are special cases of a more general algebraic AKSZ construction, in which the underlying algebras are allowed to be constrained and the presymplectic structure may be degenerate and non-regular. Within this framework, we explicitly relate Costello's formulation of the Chalmers-Siegel model to the presymplectic formulation, the latter admitting a first-principles derivation. We also construct Costello-like formulations of higher-form analogues of the Chalmers-Siegel model and of self-dual higher-spin gauge theories of Yang-Mills type, obtaining in the latter case a remarkably concise description. In so doing we propose a simple algebraic construction for the corresponding source space DGCAs underlying these examples.
ER -