费米四重态与残留引力
Fermionic quartet and vestigial gravity
AI总结：
本文通过超导体两步相变类比，提出量子引力中费米子真空可经历两次相变，先出现度规（玻色子爱因斯坦引力），后出现四脚场（爱因斯坦-嘉当引力），导致引力对费米子和玻色子作用强度不同。
摘要：
我们讨论了超导体中的两步相变，其中库珀对态与正常金属之间的中间态是4费米子凝聚体，这被称为交织的残留序。我们讨论了在自旋三重态超流$^3$He中可能存在的不同类型的残留序，以及残留相中的拓扑对象。由于在$^3$He中，序参量$A_{\alpha i}$代表了引力四脚场的类比，我们建议在量子引力中可能存在残留态。如同在超导体中一样，费米子真空可以经历两个连续的相变。在第一次相变中，度规作为四脚场的双线性组合出现，即$g_{\mu\nu} = \eta_{ab}< \hat E^a_\mu\hat E^b_\nu>$，而四脚场序参量仍然不存在，即$e_\mu^a=< \hat E^a_\mu> =0$。这对应于玻色子爱因斯坦广义相对论，它出现在费米子真空中。非零的四脚场$e_\mu^a=< \hat E^a_\mu> \neq 0$在第二次相变中出现，此时形成了一种爱因斯坦-嘉当-夏玛-基布尔四脚场引力。这表明在粒子层面上，引力对费米子和玻色子的作用强度不同。
英文摘要：
We discuss the two-step transitions in superconductors, where the intermediate state between the Cooper pair state and the normal metal is the 4-fermion condensate, which is called the intertwined vestigial order. We discuss different types of the vestigial order, which are possible in the spin-triplet superfluid $^3$He, and the topological objects in the vestigial phases. Since in $^3$He the order parameter $A_{αi}$ represents the analog of gravitational tetrads, we suggest that the vestigial states are possible in quantum gravity. As in superconductors, the fermionic vacuum can experience two consequent phase transitions. At first transition the metric appears as the bilinear combination of tetrads $g_{μν} =η_{ab}< \hat E^a_μ\hat E^b_ν>$, while the tetrad order parameter is still absent, $e_μ^a=< \hat E^a_μ> =0$. This corresponds to the bosonic Einstein general relativity, which emerges in the fermionic vacuum. The nonzero tetrads $e_μ^a=< \hat E^a_μ> \neq 0$ appear at the second transition, where a kind of the Einstein-Cartan-Sciama-Kibble tetrad gravity is formed. This suggests that on the levels of particles, gravity acts with different strength on fermions and bosons.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
