Alexander Mamekin | Searcharxiv

arXiv2026

Presymplectic BV-AKSZ and constrained DGCAs

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.

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arXiv2025

Presymplectic BV-AKSZ for $N=1$, $D=4$ Supergravity

We elaborate on the presymplectic BV-AKSZ approach to supersymmetric systems. In particular, we construct such a formulation for the $N=1$, $D=4$ supergravity by taking as a target space the Chevalley-Eilenberg complex of the super-Poincar\'e algebra which, as we demonstrate, admits an invariant presymplectic structure of degree $3$. This data encodes a full-scale Batalin-Vilkovisky formulation of the system, including a concise form of the BV master action. The important feature of (presymplectic) AKSZ models is that, at least at the level of equations of motion, they can be equivalently reformulated in the spacetime obtained by adding or eliminating contractible dimensions. For instance, the presymplectic AKSZ formulation of gravity can be lifted to the respective ``group manifold'', endowing it with the structure of a principle bundle and the Cartan connection therein, at least locally. In particular, the so-called rheonomy conditions emerge as a part of the presymplectic AKSZ equations of motion. The analogous considerations apply to supergravity and its uplift to superspace. We also study general presymplectic BV-AKSZ models related by adding or removing contractible spacetime dimensions in order to systematically relate the spacetime and superspace formulations of the same system within the AKSZ-like framework. These relations are then illustrated using the supersymmetric particle as a toy model.

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