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PreprintarXiv licencearXiv

M2 brane in AdS4× S7/ℤk: 2-loop correction to 1/2-BPS Wilson loop vs localization in ABJM theory

  • M. Beccaria
  • S. A. Kurlyand
  • A. A. Tseytlin
  • J. van Muiden
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Abstract

We study the quantization of an M2 brane wrapping AdS2× S1 inside AdS4× S7/ℤk, dual to the 1/2-BPS circular Wilson loop in ABJM theory. The classical action and the one-loop contribution were previously shown to reproduce the gauge-theory localization result. Here we extend the analysis to the two-loop order. In an adapted static and κ-symmetry gauge the world-volume action contains no cubic interaction vertices, so that the two-loop correction is determined entirely by quartic interactions and is manifestly free of logarithmic UV divergences. We find that the bosonic and fermionic contributions combine into a perfect square $ {\mathscr X}^2$ where 𝒳 is a linear combination of the bosonic and fermionic 3d Green's functions and their derivatives. The evaluation of 𝒳 requires fixing the AdS2 boundary quantization of the massless fermionic modes. With the boundary conditions selected by the preserved supersymmetry, 𝒳 vanishes and hence the complete two-loop correction is found to be zero. This result would not be consistent with identifying the M2-brane loop expansion directly with the large-N expansion of the canonical, fixed-(N,k) localization prediction. Instead, it agrees precisely with the recent proposal that the semiclassical M2-brane partition function should be matched to the gauge-theory grand-canonical ensemble, in which the Wilson loop expectation value is perturbatively one-loop exact. The vanishing of the two-loop correction thus provides a non-trivial test of this grand-canonical identification.

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Cite

BibTeXRIS
BibTeX
@misc{beccaria2026brane,
  title = {{M2 brane in AdS$_4\times S^7/\mathbb Z_k$: 2-loop correction to $\frac12$-BPS Wilson loop vs localization in ABJM theory}},
  author = {M. Beccaria and S. A. Kurlyand and A. A. Tseytlin and J. van Muiden},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.14497},
  eprint = {2609.14497},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14497},
}
RIS
TY  - UNPB
TI  - M2 brane in AdS_4× S^7/ℤ_k: 2-loop correction to 1/2-BPS Wilson loop vs localization in ABJM theory
AU  - M. Beccaria
AU  - S. A. Kurlyand
AU  - A. A. Tseytlin
AU  - J. van Muiden
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.14497
UR  - https://arxiv.org/abs/2609.14497
AB  - We study the quantization of an M2 brane wrapping AdS_2× S^1 inside AdS_4× S^7/ℤ_k, dual to the 1/2-BPS circular Wilson loop in ABJM theory. The classical action and the one-loop contribution were previously shown to reproduce the gauge-theory localization result. Here we extend the analysis to the two-loop order. In an adapted static and κ-symmetry gauge the world-volume action contains no cubic interaction vertices, so that the two-loop correction is determined entirely by quartic interactions and is manifestly free of logarithmic UV divergences. We find that the bosonic and fermionic contributions combine into a perfect square $ {\mathscr X}^2$ where 𝒳 is a linear combination of the bosonic and fermionic 3d Green's functions and their derivatives. The evaluation of 𝒳 requires fixing the AdS_2 boundary quantization of the massless fermionic modes. With the boundary conditions selected by the preserved supersymmetry, 𝒳 vanishes and hence the complete two-loop correction is found to be zero. This result would not be consistent with identifying the M2-brane loop expansion directly with the large-N expansion of the canonical, fixed-(N,k) localization prediction. Instead, it agrees precisely with the recent proposal that the semiclassical M2-brane partition function should be matched to the gauge-theory grand-canonical ensemble, in which the Wilson loop expectation value is perturbatively one-loop exact. The vanishing of the two-loop correction thus provides a non-trivial test of this grand-canonical identification.
ER  -