通过 Clifford 代数中的中心荷反常研究八元数与量子引力
Octonions and Quantum Gravity through the Central Charge Anomaly in the Clifford Algebra
AI总结：
本文基于超代数、复化八元数与 Clifford 代数构建含 AdS$_3$ 等距/量子比特对偶的量子引力理论，利用中心荷反常得到全息面积律并提出黑洞信息悖论的解决机制。
摘要：
我们推导了一种包含 AdS$_3$ 等距/量子比特对偶的量子引力理论。该理论基于齐次 AdS$_3$ 时空等距群的包络代数的一种超代数推广，并通过正则量子化同构于复化八元数代数。其前三个四元数生成元对应于一个由 $\hbar$ 量子化的 AdS$_3$ 嵌入时空，其余四个非四元数生成元则对应于一个由 $G$ 量子化的嵌入 $2+2$ Minkowski 时空。四元数代数在单态射入复化 Clifford 代数后的表达式产生了一个具有中心荷反常的二维共形算子乘积展开，这导致满足全息原理的面积律 $\hbar G$ 标度，并定义了一个“时间箭头”。这种关系使我们能够通过嵌入体的超对称破缺和共形破缺的 $\mathcal O(G)$ 变换来扩展该理论，以产生受扰动的 AdS$_3$ 时空，并用一个显式机制推导出黑洞信息悖论的解决方案。
英文摘要：
We derive a theory of quantum gravity containing an AdS$_3$ isometry/qubit duality. The theory is based on a superalgebra generalization of the enveloping algebra of the homogeneous AdS$_3$ spacetime isometry group and is isomorphic to the complexified octonion algebra through canonical quantization. Its first three quaternion generators correspond to an $\hbar$-quantized AdS$_3$ embedded spacetime and its remaining four non-quaternion generators to a $G$-quantized embedding $2+2$ Minkowski spacetime. The quaternion algebra's expression after a monomorphism into the complexified Clifford algebra produces a two-dimensional conformal operator product expansion with a central charge anomaly, which results in an area-law $\hbar G$ scaling satisfying the holographic principle and defines an "arrow of time". This relationship allows us to extend the theory through supersymmetry- and conformal-breaking $\mathcal O(G)$ transformations of the embedding to produce perturbed AdS$_3$ spacetimes and derive a resolution to the black hole information paradox with an explicit mechanism.
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。
