张量层级结构来自形变量子化
Tensor hierarchy from deformation quantisation
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中文总结 AI 辅助
通过形式形变量子化，从二阶微分分次辛流形构造出NS-NS超引力及双重场论（DFT）的完整经典运动学与动力学，扩展张量层级为编码场与恒等式的复形，并自然推广对偶群至O(D,D)×R^+。
中文摘要 AI 辅助
我们证明，对二阶微分分次辛（QP）流形的形式形变量子化产生了NS-NS超引力的完整经典运动学和动力学，或者等价地，其作为双重场论（DFT）的对偶协变表述。我们的构造将标准张量层级结构（编码规范参数及其冗余）扩展为一个复形，该复形编码物理场、场强和Bianchi恒等式。我们给出了这种复形的两种实现：1）由QP流形上函数代数构建的微分分次李代数；2）一个上链复形，它重现了文献中推测的张量层级表示，并可解释为线性化理论的经典BV复形。产生膨胀子的形变来自一个正规序的分次Moyal-Weyl星积。这自然地将对偶结构群从O(D,D)扩展为O(D,D)×R^+。最后，我们的框架通过局部双重洛伦兹不变性直接构建DFT作用，并为广义嘉当几何中的曲率张量提供了透明的代数基础。
英文摘要
We show that a formal deformation quantisation of degree-2 differential graded symplectic (QP) manifolds gives rise to the complete classical kinematics and dynamics of NS-NS supergravity, or, equivalently, its duality-covariant formulation as double field theory (DFT). Our construction extends the standard tensor hierarchy, encoding gauge parameters and their redundancies, to a complex encoding the physical fields, field strengths, and Bianchi identities. We present two realisations of such a complex: 1) a differential graded Lie algebra built from the algebra of functions on the QP-manifold; 2) a cochain complex that reproduces the tensor hierarchy representations conjectured in the literature and can be interpreted as a classical BV complex of the linearised theory. The deformation that gives rise to the dilaton comes from a normal-ordered graded Moyal--Weyl star product. This naturally extends the duality structure group from $\mathrm{O}(D,D)$ to $\mathrm{O}(D,D)\times\mathbb{R}^+$. Finally, our framework provides a direct route to constructing the DFT action via local double Lorentz invariance, and offers a transparent algebraic foundation for curvature tensors in generalised Cartan geometry.
发表机构
- Institute for Theoretical Physics (IFT), University of Wrocław（弗罗茨瓦夫大学理论物理研究所）
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