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$
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| Autores principales: | , , |
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| Formato: | Preprint |
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2026
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| _version_ | 1866917323997184000 |
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| author | Beccaria, Matteo Kurlyand, Stefan A. Tseytlin, Arkady A. |
| author_facet | Beccaria, Matteo Kurlyand, Stefan A. Tseytlin, Arkady A. |
| contents | 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: $\langle W\rangle = {2N\over \sqrt λ} I_1 ( \sqrt λ)$. Expanded in large $λ$ and expressed in terms of the AdS$_5 \times $S$^5$ string tension $T= {\sqrt λ\over 2π}$ this gives $\langle W\rangle = {\sqrt T\over 2πg_s} e^{2πT} (1- {3\over 16 π} T^{-1} + ...)$.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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08809 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | 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$ Beccaria, Matteo Kurlyand, Stefan A. Tseytlin, Arkady A. High Energy Physics - Theory 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: $\langle W\rangle = {2N\over \sqrt λ} I_1 ( \sqrt λ)$. Expanded in large $λ$ and expressed in terms of the AdS$_5 \times $S$^5$ string tension $T= {\sqrt λ\over 2π}$ this gives $\langle W\rangle = {\sqrt T\over 2πg_s} e^{2πT} (1- {3\over 16 π} T^{-1} + ...)$.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. |
| 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$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.08809 |