解析全息赝熵在助推BTZ几何中的应用
Analytic Holographic Pseudo-Entropy in a Boosted BTZ Geometry
- Shahid Beheshti University（沙希德·贝赫什蒂大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文在助推BTZ黑洞中推导全息纠缠熵的精确解析公式，并通过解析延拓将其推广至赝熵，建立了助推时空与全息赝熵的直接联系。
AI中文摘要：
我们研究了助推BTZ黑洞几何中的全息纠缠熵及其向赝熵的推广，该几何在全息上对偶于一个运动的强耦合等离子体。通过求解极值曲面方程，我们推导出全息纠缠熵作为边界区间长度、助推速度、温度和守恒量的函数的精确闭式表达式。所得精确解析公式在零助推极限下正确重现了标准热BTZ纠缠熵，并在零温度下平滑地简化为真空共形结果，从而提供了稳健的一致性检验。受洛伦兹变换产生的助推度规的非对角结构启发，我们随后研究了两种到欧几里得符号的解析延拓族。两者都需要同时延拓时间坐标和助推参数，以使欧几里得度规保持实数。如果仅延拓这两个参数，边界区间变为虚数，解析延拓后的全息纠缠熵为复值；我们将此复熵解释为助推热态赝熵的全息对偶。如果另外还延拓一个守恒荷，则边界区间保持实数，所得熵为实数。我们的构造建立了助推HEE与全息赝熵之间的直接联系，将先前为旋转BTZ几何开发的解析框架扩展到洛伦兹助推时空。
英文摘要：
We investigate holographic entanglement entropy and its generalization to pseudo-entropy in a boosted BTZ black hole geometry, which is holographically dual to a moving strongly coupled plasma. By solving the extremal surface equation, we derive an {\it exact closed-form expression} for the holographic entanglement entropy as a function of the boundary interval length, boost velocity, temperature, and conserved quantities. The resulting exact analytic formula correctly reproduces the standard thermal BTZ entanglement entropy in the vanishing-boost limit and smoothly reduces to the vacuum conformal result at zero temperature, thereby providing robust consistency checks. Motivated by the off-diagonal structure of the boosted metric arising from the Lorentz transformation, we then study two families of analytic continuations to Euclidean signature. Both require a simultaneous continuation of the time coordinate and the boost parameter so that the Euclidean metric remains real. If only these two parameters are continued, the boundary interval becomes imaginary and the analytically continued holographic entanglement entropy is complex-valued; we interpret this complex entropy as the holographic dual of pseudo-entropy for the boosted thermal state. If, in addition, a conserved charge is also continued, the boundary interval remains real and the resulting entropy is real. Our construction establishes a direct connection between boosted HEE and holographic pseudo-entropy, extending previous analytic frameworks developed for rotating BTZ geometries to Lorentz-boosted spacetimes.
