从旋量圈涌现的爱因斯坦-嘉当引力
Emergent Einstein-Cartan gravity from a spinor loop
AI总结：
该论文证明在爱因斯坦-嘉当旋量引力中，旋量圈不仅生成LL规范场动能和质量项，还生成vierbein两点函数，诱导出包含宇宙学常数、爱因斯坦-希尔伯特项、外尔平方项及挠率质量与动能项的有效作用，完成隐藏局域洛伦兹涌现引力场景。
AI中文摘要：
在不可逆 vierbein 假设下的爱因斯坦-嘉当旋量引力中，一阶变量中只有旋量在树级具有自身的动能项。任何非零背景 vierbein 都会自发破缺局域洛伦兹（LL）对称性。我们之前的工作表明，旋量圈生成 LL 规范场的动能项和质量项，将 LL 显现为隐藏的局域对称性。这里我们证明，旋量圈还生成 vierbein 两点函数，同时尊重背景规范不变性并满足真实规范不变性的 Ward-Takahashi 恒等式，对于一般坐标和 LL 对称性都是如此。与方案无关的对数发散组装了熟悉的诱导引力要素：一个宇宙学常数、一个爱因斯坦-希尔伯特项和一个外尔平方项用于度规扇区，以及一个质量和更高导数动能项用于完全反对称挠率。在 vierbein 扇区中，该挠率由线性 vierbein 涨落的反对称部分的导数承载。该部分是自发破缺 LL 对称性的潜在 Nambu-Goldstone 玻色子，其在最小耦合作用中的耦合全部由一般坐标和 LL 规范不变性固定。五个诱导项形成一个单一有效作用，对两种对称性都明显不变，完成了隐藏局域洛伦兹涌现引力场景的 vierbein 扇区。
英文摘要：
In Einstein-Cartan spinor gravity under the irreversible vierbein postulate, only the spinor among the first-order variables has a kinetic term of its own at tree level. Any nonzero background vierbein breaks the local-Lorentz (LL) symmetry spontaneously. Our previous work showed that the spinor loop generates the kinetic and mass terms of the LL gauge field, manifesting LL as a hidden local symmetry. Here we show that the spinor loop also generates the vierbein two-point function, while respecting the background gauge invariance and satisfying the Ward-Takahashi identities of the true gauge invariance, for both the general-coordinate and LL symmetries. The scheme-independent logarithmic divergence assembles the familiar induced-gravity ingredients: a cosmological constant, an Einstein-Hilbert and a Weyl-squared term for the metric sector, and a mass and a higher-derivative kinetic term for the totally antisymmetric torsion. In the vierbein sector, this torsion is carried by the derivative of the antisymmetric part of the linear vierbein fluctuation. This part is the would-be Nambu-Goldstone boson of the spontaneously broken LL symmetry, and its couplings in the minimally coupled action are all fixed by general-coordinate and LL gauge invariance. The five induced terms form a single effective action, manifestly invariant under both symmetries, completing the vierbein sector of the hidden-local-Lorentz emergent-gravity scenario.
