Dirac算符的行列式和Weyl反常：全息推导
Determinant and Weyl anomaly of Dirac operator: a holographic derivation
摘要：
我们提出了一个全息公式有关的功能行列式：费米子行列式在一个渐进的本地AdS背景下的散装旋量的单圈有效作用，和共形边界处的对偶算子的两点函数的行列式。该公式源于AdS/CFT算法，该算法将体配分函数中的量子贡献映射到边界配分函数中的子前导大N贡献。我们用这个全息图来解决谱理论和共形几何中的问题。作为一个例子，我们计算了球面上的A型Weyl反常和迭代Dirac算子的行列式，用Barnes的多重Gamma函数表示后者，并对Bär和Schopka的一个猜想有了深入的了解.
英文摘要：
We present a holographic formula relating functional determinants: the fermion determinant in the one-loop effective action of bulk spinors in an asymptotically locally AdS background, and the determinant of the two-point function of the dual operator at the conformal boundary. The formula originates from AdS/CFT heuristics that map a quantum contribution in the bulk partition function to a subleading large-N contribution in the boundary partition function. We use this holographic picture to address questions in spectral theory and conformal geometry. As an instance, we compute the type-A Weyl anomaly and the determinant of the iterated Dirac operator on round spheres, express the latter in terms of Barnes' multiple gamma function and gain insight into a conjecture by Bär and Schopka.
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