Heat kernels on cone of $Ad{S}_2$ and $k$-wound circular Wilson loop in $Ad{S}_5\times S^5$ superstring

Abstract

We compute the one-loop world-sheet correction to partition function of $Ad{S}_5\times S^5$ superstring that should be representing $k$-fundamental circular Wilson loop in planar limit. The 2d metric of the minimal surface ending on $k$-wound circle at the boundary is that of a cone of $Ad{S}_2$ with deficit $2\pi (1-k)$. We compute determinants of 2d fluctuation operators by first constructing heat kernels of scalar and spinor Laplacians on the cone using the Sommerfeld formula. The final expression for the k-dependent part of the one-loop correction has simple integral representation but is different from earlier results.

16 pages

References in corpus (4)

• Entanglement entropy, conformal invariance and extrinsic geometry
• The 1/N correction in the D3-brane description of circular Wilson loop at strong coupling
• On Renyi entropy for free conformal fields: holographic and q-analog recipes
• Heat Kernel for Simply-Connected Riemann Surfaces

Cited by in corpus (2)

• Precision calculation of 1/4-BPS Wilson loops in AdS${}_5\times S^5$
• Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in $Ad{S}_5\times S^5$