Higher Spin Gravities and Presymplectic AKSZ Models

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 …

类框架拉格朗日函数和前辛AKSZ型西格玛模型

Frame-like Lagrangians and presymplectic AKSZ-type sigma models

我们研究超几何结构的框架样拉格朗日。我们证明了对于n维时空中的理论，框架样拉格朗日量及其规范对称性都被编码在目标超流形中，该目标超流形具有奇向量场、鬼度n-1的闭2-形式和鬼度n的标量势.这些结构满足一组相容性条件，确保了理论的规范不变性。拉格朗日量和规范对称性具有与AKSZ西格玛模型相同的结构，因此类框架表述可以看作是它的前辛推广。与传统的AKSZ模型相比，泛化允许描述有限维目标空间中具有局部自由度的系统。我们认为，所提出的框架样的方法是直接相关的德Donder-Weyl多动量哈密顿形式主义。除了爱因斯坦-杨-米尔斯理论这样的标准场论例子外，我们还考虑了自由高自旋场、多标架引力和参数化系统。特别是，我们提出了框架般的行动自由完全对称的无质量领域，涉及所有更高的自旋连接在平等的基础上。

Presymplectic AKSZ formulation of Einstein gravity

Any local gauge theory can be represented as an AKSZ sigma model (upon parameterization if necessary). However, for non-topological models in dimension higher than 1 the target space is necessarily infinite-dimensional. The interesting alternative known for some time is to allow for degenerate presymplectic structure in the target space. This leads to a very concise AKSZ-like representation for frame-like Lagrangians of gauge systems. In this work we concentrate on Einstein gravity and show that not only the Lagrangian but also the full-scale Batalin--Vilkovisky formulation is naturally encode…

预辛BV-AKSZ结构用于N=1，D=4超引力

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

本文提出预辛BV-AKSZ方法用于N=1，D=4超引力，通过构建超庞加莱代数的Chevalley-Eilenberg复形，实现时空与超时空表述的联系。

预辛BV-AKSZ方法中的一致形变

Consistent deformations in the presymplectic BV-AKSZ approach

本文基于预辛BV-AKSZ公式开发有限维空间框架，避免商空间操作，通过预辛规范PDE结构分析局域规范理论一致相互作用，扩展框架类方法并重新推导Chern-Simons和YM理论。

预辛BV-AKSZ与约束DGCA

Presymplectic BV-AKSZ and constrained DGCAs

本文统一了两种AKSZ推广途径，提出约束DGCA与退化预辛结构的代数框架，并给出Chalmers-Siegel模型及其高阶形式与自对偶高阶自旋理论的简洁构造。