论文标题
来自可整合自旋链的2D黑洞Sigma模型的平衡密度矩阵
Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain
论文作者
论文摘要
这项工作涉及量子Lorentzian和Euclidean黑洞非线性Sigma模型。对于Euclidean Black Sigma模型，提出了平衡密度矩阵，该矩阵从2001年Maldacena，Ooguri和Son的论文中复制了模块化不变分区函数。对于Lorentzian Black Hole Sigma模型，使用其公式作为测量的$ {\ rm SL}（2，\ Mathbb {r}）$ WZW模型，我们描述了其状态空间的线性和遗传结构，并提出了平衡密度矩阵的表达式。我们的分析以某种关键，可集成的自旋链的研究结果为指导。在缩放限制中，后者表现出Lorentzian Black Sigma模型的关键特征，包括相同的全局对称性，相同的延长结构对称性代数和连续的保形尺寸。
This work concerns the quantum Lorentzian and Euclidean black hole non-linear sigma models. For the Euclidean black hole sigma model an equilibrium density matrix is proposed, which reproduces the modular invariant partition function from the 2001 paper of Maldacena, Ooguri and Son. For the Lorentzian black hole sigma model, using its formulation as a gauged ${\rm SL}(2,\mathbb{R})$ WZW model, we describe the linear and Hermitian structure of its space of states and also propose an expression for the equilibrium density matrix. Our analysis is guided by the results of the study of a certain critical, integrable spin chain. In the scaling limit, the latter exhibits the key features of the Lorentzian black hole sigma model including the same global symmetries, the same algebra of extended conformal symmetry and a continuous spectrum of conformal dimensions.
