任意维度下自由无质量费米子的精确互信息
Exact mutual information for free massless fermions in any dimension
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中文总结 AI 辅助
该研究推导了任意维自由无质量Dirac场及四维无质量Rarita-Schwinger场的球形区域间Rényi互信息精确表达式，通过二维AdS有质量费米子对应结合Painlevé方程求解，得到长短距离渐近行为及相关系数。
中文摘要 AI 辅助
我们得到了d维时空中自由无质量Dirac场，以及d=4维中无质量Rarita-Schwinger场的两个球形区域之间Rényi互信息（RMI）的精确表达式。我们将母理论的球对称维数约化中的每个角动量模式，对应为二维反德西特空间（AdS）中的有质量Dirac费米子。对于任意Rényi指数n，每个模式的RMI都可通过Painlevé微分方程的解进行解析计算。我们探究了该结果的长距离与短距离渐近行为，此情形下对各模式的求和可被显式计算。由此，我们能够得到任意n下d维长距离展开的次领头阶贡献，还能提取短距离区域内n=1情形下的面积系数与对数系数。
英文摘要
We obtain an exact expression for the Rényi mutual information (RMI) between two spherical regions for a free, massless Dirac field in $d$ spacetime dimensions and for a massless Rarita-Schwinger field in $d=4$. We identify each angular momentum mode in the spherical dimensional reduction of the parent theory with a massive Dirac fermion in two dimensional anti-de Sitter space (AdS). The RMI for each mode can be computed analytically for any Rényi index $n$ in terms of solutions of a Painlevé differential equation. We explore the long and short distance asymptotics of the result, where the sum over modes can be computed explicitly. As a result we are able to find subleading contributions to the long distance expansion in $d$ dimensions for arbitrary $n$, as well as to extract the area and logarithmic coefficients for the case $n=1$ in the short distance regime.
