arXiv subjects

Ivan Dneprov

Publications and source records attributed to Ivan Dneprov.

4 recordsLinked to original sources

arXiv2026

Asymptotic boundary structure of Lagrangian gauge theories

Given a local gauge theory on spacetime with boundary, it naturally defines another gauge theory which can be regarded as a theory of the boundary values. For Lagrangian theories, it comes equipped with the presymplectic structure which can be used to define one or another version of Hamiltonian-like formulation of the initial model. This relation is especially manifest for AKSZ sigma models and more-generally gauge PDEs with compatible presymplectic structure in which case the boundary system is again a gauge PDE with presymplectic structure. In the context of (flat space) holography one is interested in boundaries at infinity, also known as asymptotic boundaries. The gauge PDE framework naturally extends to this setup, resulting in the notion of gauge PDE with asymptotic boundaries. Although this works perfectly well at the level of equations of motion, the extension to Lagrangian systems appears quite subtle because the presymplectic structure capturing the Lagrangian is divergent at the boundary. We show that any $Q$-cocycle in the bulk (and presymplectic structure in particular) determines a pair of compatible $Q$-cocycles of the boundary gauge PDE: the renormalized one of the same ghost-degree, and the anomaly cocycle of degree one lower. For the latter, the construction is somewhat analogous to the residue map known in the context of b-geometry. The general formalism is exemplified by scalar and Maxwell fields on AdS and Minkowski spaces. It turns out that in the AdS case the natural action determined by the anomaly presymplectic structure is precisely the one known as the holographic Weyl anomaly in the AdS/CFT context while its null-infinity counterpart was known in a few very particular cases only.

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arXiv2026

Background fields in the presymplectic BV-AKSZ approach

The Batalin-Vilkovisky formulation of a general local gauge theory can be encoded in the structure of a so-called presymplectic gauge PDE -- an almost-$Q$ bundle over the spacetime exterior algebra, equipped with a compatible presymplectic structure. In the case of a trivial bundle and an invertible presymplectic structure, this reduces to the well-known AKSZ sigma model construction. We develop an extension of the presympletic BV-AKSZ approach to describe local gauge theories with background fields. It turns out that such theories correspond to presymplectic gauge PDEs whose base spaces are again gauge PDEs describing background fields. As such, the geometric structure is that of a bundle over a bundle over a given spacetime. Gauge PDEs over backgrounds arise naturally when studying linearisation, coupling (gauge) fields to background geometry, gauging global symmetries, etc. Less obvious examples involve parametrised systems, Fedosov equations, and the so-called homogeneous (presymplectic) gauge PDEs. The latter are the gauge-invariant generalisations of the familiar homogeneous PDEs and they provide a very concise description of gauge fields on homogeneous spaces such as higher spin gauge fields on Minkowski, (A)dS, and conformal spaces. Finally, we briefly discuss how the higher-form symmetries and their gauging fit into the framework using the simplest example of the Maxwell field.

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arXiv2024

Presymplectic minimal models of local gauge theories

We elaborate on the recently proposed notion of a weak presymplectic gauge PDE. It is a $\mathbb{Z}$-graded bundle over the space-time manifold, equipped with a degree $1$ vector field and a compatible graded presymplectic structure. This geometrical data naturally defines a Lagrangian gauge field theory. Moreover, it encodes not only the Lagrangian of the theory but also its full-scale Batalin-Vilkovisky (BV) formulation. In particular, the respective field-antifield space arises as a symplectic quotient of the super-jet bundle of the initial fiber bundle. A remarkable property of this approach is that among the variety of presymplectic gauge PDEs encoding a given gauge theory we can pick a minimal one that usually turns out to be finite-dimensional, and unique in a certain sense. The approach can be considered as an extension of the familiar AKSZ construction to not necessarily topological and diffeomorphism-invariant theories. We present a variety of examples including $p$-forms, chiral Yang-Mills theory, Holst gravity, and conformal gravity. We also explain the explicit relation to the non-BV-BRST version of the formalism, which happens to be closely related to the covariant phase space and the multisymplectic approaches.

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arXiv2022

Presymplectic BV-AKSZ formulation of Conformal Gravity

We elaborate on the presymplectic BV-AKSZ approach to local gauge theories and apply it to conformal gravity. More specifically, we identify a compatible presymplectic structure on the minimal model of the total BRST complex of this theory and show that together with the BRST differential it determines a full-scale BV formulation for a specific frame-like action which seems to be previously unknown. Remarkably, the underlying frame-like description requires no artificial off-shell constraints. Instead, the action becomes equivalent to the usual conformal gravity one, upon gauging away all the variables belonging to the kernel of the presymplectic structure. Finally, we show how the presymplectic BV-AKSZ approach extends to generic gauge theories.

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