AI 中文总结
研究二维反德西特空间单味量子电动力学中的禁闭与屏蔽，通过玻色化等方法得到静态势，提出协变离散化方案，用张量网络模拟验证解析预测，解决了相关模糊性并匹配连续统预测。
AI 中文摘要
我们分析了二维反德西特空间（AdS₂）上单味量子电动力学（QED₂）中的禁闭和屏蔽现象，考虑有无施瓦西黑洞的情况，包括连续统和晶格两种情形。该理论在两个适应不同优选时间坐标选择的框架中表述：与博尔韦尔真空相关的施瓦西框架和与SL(2,R)不变真空相关的全局AdS₂框架。在无质量极限下，通过玻色化在零温和有限温度下得到外部电荷 - 反电荷对之间的静态势。减去位置相关的探针自能后，势在测地线分离趋于无穷时保持有限，表明理论是屏蔽的。这与动态费米子对U(1)电单形式对称性的明确破坏一致，解决了早期处理中因将静态势与未减去的基态能量等同而产生的禁闭/屏蔽模糊性。为验证连续统分析，我们提出一种协变离散化方案，用于在晶格上的弯曲时空中放置费米子，同时确保在连续统极限中恢复自旋和规范连接的连续统性质。此构造解决了弯曲背景下晶格费米子现有文献中的模糊性，并为我们的张量网络模拟提供了基础。使用矩阵乘积态假设，我们证实了对AdS₂中相图的解析预测。我们对不同费米子质量的静态势和电通量管轮廓进行了广泛的数值模拟，并与连续统预测相匹配。
英文摘要
We analyze confinement and screening in single-flavor quantum electrodynamics (QED$_2$) on two-dimensional anti-de Sitter space (AdS$_2$), with and without a Schwarzschild black hole, both in the continuum and on the lattice. The theory is formulated in two frames adapted to distinct choices of a preferred time coordinate: the Schwarzschild frame, associated with the Boulware vacuum, and the global AdS$_2$ frame, associated with the $\mathrm{SL}(2,\mathbb{R})$-invariant vacuum. In the massless limit, the static potential between an external charge-anticharge pair is obtained in closed form by bosonization, at both zero and finite temperature. After subtraction of the position-dependent probe self-energies, which, unlike in flat space, are not constant, the potential remains finite as the geodesic separation is taken to infinity, establishing that the theory is screened. This is consistent with the explicit breaking of the $\mathrm{U}(1)$ electric one-form symmetry by the dynamical fermions, and resolves a confining/screening ambiguity in earlier treatments that identify the static potential with the unsubtracted ground-state energy. To validate the continuum analysis, we propose a covariant discretization scheme for placing fermions in curved spacetime on the lattice while ensuring that the continuum properties of the spin and gauge connections are restored in the continuum limit. This construction resolves ambiguities in the existing literature on lattice fermions in curved backgrounds and provides the foundation for our tensor-network simulations. Using a matrix product state ansatz, we confirm our analytical predictions for the phase diagram in AdS$_2$. We perform extensive numerical simulations of the static potential and the electric flux-tube profile for varying fermion masses, which we match to the continuum prediction.
Comments40 pages, 7 figures
