Heat kernels on cone of $AdS_2$ and $k$-wound circular Wilson loop in $AdS_5 \times S^5$ superstring

R. Bergamin; A. A. Tseytlin

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arXiv · 1510.06894

Heat kernels on cone of $AdS_2$ and $k$-wound circular Wilson loop in $AdS_5 \times S^5$ superstring

R. Bergamin·A. A. Tseytlin

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Abstract

We compute the one-loop world-sheet correction to partition function of $AdS_5 \times S^5$ 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 $AdS_2$ with deficit $2π(1-k)$. 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.

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R. Bergamin, A. A. Tseytlin. 2015-10-23. Heat kernels on cone of $AdS_2$ and $k$-wound circular Wilson loop in $AdS_5 \times S^5$ superstring. https://arxiv.org/abs/1510.06894

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