One loop partition function in AdS_3/CFT_2

Abstract

The 1-loop partition function of the handle-body solutions in the AdS${}_3$ gravity have been derived some years ago using the heat-kernel and the method of images. In the semiclassical limit, such partition function should correspond to the order $O(c^0)$ part in the partition function of dual conformal field theory on the boundary Riemann surface. The higher genus partition function could be computed by the multi-point functions in the Riemann sphere via sewing prescription. In the large central charge limit, to the leading order of $c$, the multi-point function is further simplified to be a summation over the product of two-point functions, which may form links. Each link is in one-to-one correspondence with the conjugacy class of the Schottky group of the Riemann surface. Moreover, the value of a link is determined by the eigenvalue of the element in the conjugate class. This allows us to reproduce exactly the gravitational 1-loop partition function. The proof can be generalized to the higher spin gravity and its dual CFT.

30 pages, 8 figures; typos corrected, more clarifications, references and acknowledgements added

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• Holographic Description of 2D Conformal Block in Semi-classical Limit
• Short interval expansion of Rényi entropy on torus
• On one-loop entanglement entropy of two short intervals from OPE of twist operators
• Holographic Entanglement Entropy For a Large Class of States in 2D CFT
• Rényi Mutual Information for Free Scalar in Even Dimensions
• Higher spin entanglement entropy at finite temperature with chemical potential
• Holographic Rényi entropy for two-dimensional N=(1,1) superconformal field theory
• Corrections to holographic entanglement plateau
• Holographic Rényi entropy for two-dimensional $\mathcal{N}$=(2,2) superconformal field theory
• Black hole solutions of three dimensional E${}_6$-gravity
• Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT
• Holographic Mutual Information of Two Disjoint Spheres