dorsal/arxiv
View SchemaStrong coupling expansion of $1\over 2$ BPS Wilson loop in SYM theory and 2-loop Green-Schwarz string in AdS$_5 \times $S$^5$
| Authors | Matteo Beccaria, Stefan A. Kurlyand, Arkady A. Tseytlin |
|---|---|
| Categories | |
| ArXiv ID | 2601.08809vv2 |
| URL | https://arxiv.org/abs/2601.08809 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
The exact localization result for the expectation value of the $1\over 2$ BPS circular Wilson loop in ${\cal N}=4$ SYM theory is given in the planar limit by the famous Bessel function expression: $\langle W\rangle = {2N\over \sqrt \lambda } I_1 ( \sqrt \lambda)$. Expanded in large $\lambda$ and expressed in terms of the AdS$_5 \times $S$^5$ string tension $T= {\sqrt \lambda \over 2\pi}$ this gives $\langle W\rangle = {\sqrt T\over 2\pi g_s} e^{2\pi T} (1- {3\over 16 \pi} T^{-1} + ...)$.The exponential is matched by the value of the action of the string with the AdS$_2$ world volume while the prefactor comes from the 1-loop GS string correction. Here we address the question of how the subleading $T^{-1}$ term could be reproduced by the 2-loop correction in the corresponding partition function of the AdS$_5 \times $S$^5$ GS string expanded near the AdS$_2$ minimal surface. We find that the string correction contains a non-zero UV logarithmic divergence implying that comparison with the SYM result requires a particular subtraction prescription. We discuss implications of this conclusion for checking the AdS/CFT duality at strong coupling.
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"abstract": "The exact localization result for the expectation value of the $1\\over 2$ BPS circular Wilson loop in ${\\cal N}=4$ SYM theory is given in the planar limit by the famous Bessel function expression: $\\langle W\\rangle = {2N\\over \\sqrt \\lambda } I_1 ( \\sqrt \\lambda)$. Expanded in large $\\lambda$ and expressed in terms of the AdS$_5 \\times $S$^5$ string tension $T= {\\sqrt \\lambda \\over 2\\pi}$ this gives $\\langle W\\rangle = {\\sqrt T\\over 2\\pi g_s} e^{2\\pi T} (1- {3\\over 16 \\pi} T^{-1} + ...)$.The exponential is matched by the value of the action of the string with the AdS$_2$ world volume while the prefactor comes from the 1-loop GS string correction. Here we address the question of how the subleading $T^{-1}$ term could be reproduced by the 2-loop correction in the corresponding partition function of the AdS$_5 \\times $S$^5$ GS string expanded near the AdS$_2$ minimal surface. We find that the string correction contains a non-zero UV logarithmic divergence implying that comparison with the SYM result requires a particular subtraction prescription. We discuss implications of this conclusion for checking the AdS/CFT duality at strong coupling.",
"arxiv_id": "2601.08809",
"authors": [
"Matteo Beccaria",
"Stefan A. Kurlyand",
"Arkady A. Tseytlin"
],
"categories": [
"hep-th"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Strong coupling expansion of $1\\over 2$ BPS Wilson loop in SYM theory and 2-loop Green-Schwarz string in AdS$_5 \\times $S$^5$",
"url": "https://arxiv.org/abs/2601.08809",
"version": "v2"
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