标题： 量子全息表面反常 显示英文标题

标题： Quantum holographic surface anomalies

摘要： 表面算符的期望值会受到对数发散的影响，这反映了共形异常。 在全息设置中，其中表面算符可以通过$AdS$中的最小曲面来计算，异常的主要贡献来自于该最小曲面的经典作用量（或面积）中的发散。 我们研究由于最小曲面的量子涨落带来的次主导修正。 就像面积中的发散不需要全局解，只需要边界附近的分析一样，对于量子修正也是如此。 我们研究涨落行列式的渐近形式，并展示如何使用热核来计算量子异常。 在描述 6d 中${\cal N}=(2,0)$理论中表面算符的 M2-膜情况下，我们对一环行列式的计算重现了通过更间接方法找到的异常表达式。 显示英文摘要

摘要： Expectation values of surface operators suffer from logarithmic divergences reflecting a conformal anomaly. In a holographic setting, where surface operators can be computed by a minimal surface in $AdS$, the leading contribution to the anomaly comes from a divergence in the classical action (or area) of the minimal surface. We study the subleading correction to it due to quantum fluctuations of the minimal surface. In the same way that the divergence in the area does not require a global solution but only a near-boundary analysis, the same holds for the quantum corrections. We study the asymptotic form of the fluctuation determinant and show how to use the heat kernel to calculate the quantum anomaly. In the case of M2-branes describing surface operators in the ${\cal N}=(2,0)$ theory in 6d, our calculation of the one-loop determinant reproduces expressions for the anomaly that have been found by less direct methods.