One loop partition function in AdS_3/CFT_2

Understand

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.