二次度规仿射引力中的射影对称性及其破缺

中文摘要 AI 辅助

我们研究了四维宇称偶度规仿射引力中的广义射影对称性及其破缺，考虑的作用量在曲率上是线性的，在挠率和非度规性上至多是二次的。我们推导了广义射影变换对仿射几何不可约分量的作用，并确定了定义轴向、度规迹和完全射影不变理论的耦合关系。完全不变性将12个引力系数约化为五参数族，并为联络方程生成四个矢量诺特恒等式。射影不变性使联络算子奇异，因此我们发展了一种对称自适应方法来求解其真空场方程。然后我们分析了与狄拉克、电磁和复克莱因-戈登场的耦合。局域精确轴向射影变换对应于经典层面上无质量费米子的手性旋转，而余向量的组合充当阿贝尔联络，将局域精确矢量射影代表与标量U(1)对称性联系起来。标准麦克斯韦理论独立于仿射联络，而依赖于挠度的类麦克斯韦扩展可以通过补偿施图克尔伯格场来同时保持电磁和射影不变性。精确引力射影不变性使相应的联络方向非动力学，并迫使为其提供源的物质流消失。受控的显式破缺提升这些零模并将其转化为辅助场。因此，射影对称性为识别仿射规范模式、约束物质耦合以及将引力扇区中的对称性破缺与有效物质相互作用联系起来提供了统一原理。

英文摘要

We investigate generalized projective symmetry and its breaking in four-dimensional parity-even metric-affine gravity, considering an action linear in curvature and at most quadratic in torsion and nonmetricity. We derive the action of the generalized projective transformation on the irreducible components of the affine geometry and determine the coupling relations defining the axial, metric-trace, and fully projectively invariant theories. Complete invariance reduces the $12$ gravitational coefficients to a five-parameter family and generates four vectorial Noether identities for the connection equations. Projective invariance makes the connection operator singular, thus we develop a symmetry-adapted method for solving its vacuum field equations. We then analyze couplings to Dirac, electromagnetic, and complex Klein-Gordon fields. Locally exact axial-projective transformations correspond to chiral rotations for massless fermions at the classical level, while a combination of covectors acts as an Abelian connection linking a locally exact vector-projective representative to scalar $U(1)$ symmetry. Standard Maxwell theory is independent of the affine connection, whereas a torsion-dependent Maxwell-like extension can preserve both electromagnetic and projective invariance through compensating Stückelberg fields. Exact gravitational projective invariance makes the corresponding connection directions nondynamical and forces matter currents sourcing them to vanish. Controlled explicit breaking lifts these zero modes and converts them into auxiliary fields. Thus, projective symmetry provides a unified principle for identifying affine gauge modes, constraining matter couplings, and relating symmetry breaking in the gravitational sector to effective matter interactions.

发表机构

• Scuola Superiore Meridionale（南方高等学院）
• Istituto Nazionale di Fisica Nucleare, Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）
• University of Tartu（塔尔图大学）

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