自旋(7)-瞬子的拓扑量子场论

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-08-22 DOI:10.1016/j.geomphys.2025.105630

Rafael Herrera , Sergio A. Holguín Cardona , Alexander Quintero Vélez

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引用次数: 0

摘要

基于8维流形上自旋(7)-瞬子的模空间，构造了拓扑量子场论。利用Mathai-Quillen形式主义，我们推导出了纯几何形式的理论作用，这与先前文献中的结果一致。然后，我们在AKSZ形式体系中重新表述理论，获得Batalin-Vilkovisky作用，在规范固定之后，与我们的Mathai-Quillen结构相匹配，同时使BRST对称显式并为经典可观测物提供自然框架。我们还表明，Batalin-Vilkovisky作用可以优雅地重新定义为chen - simons类型理论。

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A topological quantum field theory for Spin(7)-instantons

We construct a topological quantum field theory based on the moduli space of

Spin (7)

-instantons on 8-dimensional manifolds. Using the Mathai-Quillen formalism, we derive the action of the theory in purely geometric terms, which coincides with prior results in the literature. We then reformulate the theory within the AKSZ formalism, obtaining a Batalin–Vilkovisky action that, after gauge fixing, matches our Mathai-Quillen construction while making the BRST symmetry explicit and providing a natural framework for classical observables. We also show that the Batalin–Vilkovisky action can be elegantly recast as a Chern–Simons type theory.

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity