来自焊接手征超联络的引力与物质
Gravity and Matter from Soldered Chiral Superconnections
AI总结：
该研究通过手征规范联络与克利福德值标架重新表述四维手征引力，构造规范协变微分形式，重现含宇宙学项的爱因斯坦-嘉当-霍斯特引力，还分析了相关物质 ansatz 的性质。
AI中文摘要：
我们基于手征规范联络与克利福德值标架，给出四维手征引力的一种重新表述。由 $e^a \gamma_a$ 生成的外代数，结合规范曲率 $F$，为规范协变微分形式提供了自然且系统的构造。我们证明，手征作用量的适当组合可重现带有宇宙学项的爱因斯坦-嘉当-霍斯特引力。原始超联络不变量仅给出代数费米子方程，因此费米子一元形式不传播，反而在两种手征性之间产生类质量混合。旋量传播由旋量 BF 型项提供，该项在物质 ansatz（近似）下简化为标准的一阶外尔动能作用量，包含挠率耦合。我们还综述了物质 ansatz 的对称性与变分性质，包括其洛伦兹等变性、与残余超对称和扭量旋子的关系，以及约化场方程与非约化场方程之间的联系。
英文摘要：
We present a reformulation of four-dimensional chiral gravity in terms of a chiral gauge connection and a Clifford-valued coframe. The exterior algebra generated by $e^a γ_a$, together with the gauge curvature $F$, provides a natural and systematic construction of gauge-covariant differential forms. We show that suitable combinations of the chiral actions reproduce Einstein--Cartan--Holst gravity with a cosmological term. The original superconnection invariants yield only algebraic fermionic equations, so the fermionic one-forms do not propagate but instead generate a mass-like mixing between the two chiralities. Spinor propagation is supplied by a spinorial BF-type term, which under the matter ansatz reduces to the standard first-order Weyl kinetic action, including the torsion coupling. We also review the symmetry and variational properties of the matter ansatz, including its Lorentz equivariance, its relation to residual supersymmetry and twistor spinors, and the connection between the reduced and unrestricted field equations.
