论文标题
RICCI流量的拓扑量子重力的几何形状
The Geometry of Time in Topological Quantum Gravity of the Ricci Flow
论文作者
论文摘要
我们继续研究与Riemannian歧管上的Ricci流动方程家族相关的拓扑非同性量子重力。这种拓扑引力是同类类型的，它表现出$ {\ cal n} = 2 $扩展的brst对称性。在以前的工作中，我们在适当的非依赖性$ {\ cal n} = 2 $ superspace中以两个步骤的过程构建了这一理论，首先提出了空间度量$ g_ {ij} $的拓扑理论，然后添加$ n $ n $ n $ n $ n^i $ n $ n $ n $ n $ n^i $ n^i $ n^i $ n^i $ n^i $ n^i $ n $ n^i $ n^i $ n^i $ n^i $ n^i $ n^i $ n^i $ n^i $ n^i $ n^i $的拓扑理论差异性。在与佩雷尔曼（Perelman）的里奇（Ricci）流程理论有关的关系中，佩雷尔曼（Perelman）的dilaton的作用是通过我们的不可射击的失误扮演的。 Here we demonstrate that this construction is equivalent to a standard one-step BRST gauge-fixing of a theory whose fields are $g_{ij}$, $n^i$ and $n$, and whose gauge symmetries consist of (i) the topological deformations of $g_{ij}$, and (ii) the ultralocal nonrelativistic limit of spacetime diffeomorphisms.我们的超空间建设的增压$ Q $扮演了BRST CHALL的角色。时空的差异对称性以有趣的“移动”形式出现，这对于当前拓扑环境之外的非递归量子重力可能具有更广泛的兴趣。与保护叶面的时空差异形态相反，本文中标识的仪表对称性可以按时进行，这清楚地表明，该理论没有局部传播的自由度。我们指出了对同一理论的有趣的双重解释，是对超级时空差异的双副本的量表修复，鬼魂和抗臭彼得的角色互换，第二个增压$ \ bar q $ $ {\ cal n} = 2 $ supergebra扮演了brst of brst of the brst of the Brst of the Brst of brst of brst of brst of brst of brst of brst of the brst。
We continue the study of topological nonrelativistic quantum gravity associated with a family of Ricci flow equations on Riemannian manifolds. This topological gravity is of the cohomological type, and it exhibits an ${\cal N}=2$ extended BRST symmetry. In our previous work, we constructed this theory in a two-step procedure in the appropriate nonrelativistic ${\cal N}=2$ superspace, first presenting a topological theory of the spatial metric $g_{ij}$, and then adding the superspace versions of the lapse and shift variables $n$ and $n^i$ while gauging the symmetries of foliation-preserving spacetime diffeomorphisms. In the relation to Perelman's theory of the Ricci flow, the role of Perelman's dilaton is played by our nonprojectable lapse. Here we demonstrate that this construction is equivalent to a standard one-step BRST gauge-fixing of a theory whose fields are $g_{ij}$, $n^i$ and $n$, and whose gauge symmetries consist of (i) the topological deformations of $g_{ij}$, and (ii) the ultralocal nonrelativistic limit of spacetime diffeomorphisms. The supercharge $Q$ of our superspace construction plays the role of the BRST charge. The spacetime diffeomorphism symmetries appear in an interestingly "shifted" form, which may be of broader interest for nonrelativistic quantum gravity outside of the present topological context. In contrast to the foliation-preserving spacetime diffeomorphisms, the gauge symmetries identified in this paper act nonprojectably on time, making it clear that this theory has no local propagating degrees of freedom. We point out an intriguing dual interpretation of the same theory, as a gauge fixing of a dual copy of ultralocal spacetime diffeomorphisms, with the role of ghosts and antighosts interchanged and the second supercharge $\bar Q$ of the ${\cal N}=2$ superalgebra playing the role of the BRST charge in the dual picture.
