Loop quantum gravity boundary dynamics and SL(2,C) gauge theory
Loop quantum gravity boundary dynamics and SL(2,C) gauge theory
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环量子引力边界动力学和SL(2,C)规范理论
DOI：
10.1088/1361-6382/ac03f8
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发表时间：
2021
影响因子：
3.5
通讯作者：
E. Livine
中科院分区：
文献类型：
--
作者：
E. Livine
在寻求量子引力的全息表述的背景下，我们研究了圈量子引力的基本边界理论结构。在3 + 1维时空中，边界理论存在于2 + 1维类时边界上，并被认为描述了存在于二维空间边界（即时空角）上的引力边界模（“边缘模”）的时间演化。我们不分析广义相对论的边界结构和它们的量子化，而是专注于研究哪些边界理论可以被标准圈量子引力形式主义和自旋网络态所支持。聚焦于“电”激发量子的面积生活在角落里，我们制定他们的动力学经典旋量变量，我们表明，多项式哈密顿耦合常数可以理解为2 + 1维类时边界上的背景度量的组件。这导致了一个猜想的边界哈密顿量和边界度规状态之间的更深层次的对应关系。我们进一步表明，一个可以重新制定的量子面积数据的SL（2，C）连接，运输的旋量的边界表面上，其SU（2）的分量将定义“磁”激发（切向Ashtekar-Barbero连接），从而打开大门，写圈量子引力边界动力学作为一个2 + 1维SL（2，C）规范理论。
In the context of the quest for a holographic formulation of quantum gravity, we investigate the basic boundary theory structure for loop quantum gravity. In 3 + 1 space-time dimensions, the boundary theory lives on the 2 + 1-dimensional time-like boundary and is supposed to describe the time evolution of gravitational boundary modes—‘edge modes’—living on the two-dimensional boundary of space, i.e. the space-time corner. We do not analyse the boundary structures of general relativity and their quantization, and focus instead on investigating which boundary theories can be supported by the standard loop quantum gravity formalism and spin network states. Focussing on ‘electric’ excitations—quanta of area—living on the corner, we formulate their dynamics in terms of classical spinor variables and we show that the coupling constants of a polynomial Hamiltonian can be understood as the components of a background metric on the 2 + 1-dimensional time-like boundary. This leads to a conjecture of a deeper correspondence between boundary Hamiltonian and boundary metric states. We further show that one can reformulate the quanta of area data in terms of a SL(2,C) connection, transporting the spinors on the boundary surface and whose SU(2) component would define ‘magnetic’ excitations (tangential Ashtekar–Barbero connection), thereby opening the door to writing the loop quantum gravity boundary dynamics as a 2 + 1-dimensional SL(2,C) gauge theory.
影响因子：
3.5
作者：
Bahr B;Dittrich B;Geiller M.
通讯作者：
Geiller M.