发表机构
Abdus Salam Centre for Theoretical Physics; Imperial College London; ITMP of MSU; Lebedev Inst.（阿卜杜勒·萨拉姆理论物理中心; 伦敦帝国理工学院; 莫斯科国立大学理论与数学物理研究所; 列别捷夫研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究M2膜瞬子S^3/Z_k在AdS_4×S^7/Z_k中的2圈配分函数修正，对应ABJM自由能的非微扰大N贡献。发现k>2时4顶点贡献的超越k依赖被集体坐标雅可比行列式抵消，超对称分离下残余有理项消失，猜想1圈结果精确。
AI 中文摘要
正如 arXiv:2609.14497 所示，包裹在 $\mathrm{AdS}_4\times S^7/\mathbb{Z}_k$ 内的 $\mathrm{AdS}_2\times S^1$ 上的 M2 膜配分函数的 2 圈修正为零，这与 arXiv:2505.21633 的猜想所预测的 ABJM 理论中巨正则系综下 $\frac{1}{2}$-BPS 威尔逊圈的局域化预言一致。在此我们研究 M2 膜瞬子 $S^3/\mathbb Z_k\subset S^7/\mathbb Z_k$ 情形下的 2 圈修正，该瞬子对偶于 3 球面上 ABJM 自由能的非微扰大 $N$ 贡献。arXiv:2307.14112 已证明 1 圈瞬子贡献与局域化预言匹配。2 圈计算因玻色子和费米子零模的存在而变得复杂，这需要使用投影格林函数并考虑集体坐标雅可比行列式。除了 M2 膜作用量中 4 顶点贡献外，雅可比行列式还提供了非平凡的 2 圈贡献。我们发现对于 $k>2$，无论费米子零模与量子场如何分离，4 顶点贡献的超越性 $k$ 依赖性都被雅可比行列式抵消。在超对称选择的分离方式下（即集体坐标与量子场形成独立的超多重态），残余的有理项消失。我们猜想，对集体坐标的剩余积分仅贡献于配分函数的整体归一化，因此 1 圈结果是精确的。对于 $k=1$，四次顶点贡献简化为运动方程项，如同 arXiv:2511.22306 中 ${\rm AdS}_3 \subset {\rm AdS}_7 \times S^4$ 的情形，后者通过形式解析延拓与 $S^3 \subset {\rm AdS}_4 \times S^7$ 情形相关。
英文摘要
As was shown in arXiv:2609.14497, the 2-loop $ {\rm T}^{-1}_2$ correction to the partition function of M2 brane wrapping $\mathrm{AdS}_2\times S^1$ inside $\mathrm{AdS}_4\times S^7/\mathbb{Z}_k$ vanishes. This is in agreement with the localization prediction for $\frac{1}{2}$-BPS circular Wilson loop in ABJM theory interpreted in the grand-canonical ensemble according to the conjecture of arXiv:2505.21633. Here we study the ${\rm T}^{-1}_2$ correction for the M2 brane instanton wrapping $S^3/\mathbb Z_k\subset S^7/\mathbb Z_k$ dual to the leading non-perturbative large $N$ contribution to the ABJM free energy on 3-sphere. The 1-loop instanton M2 brane partition function was shown in arXiv:2307.14112 to match the localization prediction. The 2-loop computation is complicated by the presence of bosonic and fermionic zero modes, which requires to integrate over the collective coordinates. The collective-coordinate Jacobian provides a non-trivial ${\rm T}^{-1}_2$ contribution in addition to the one of the quartic interaction vertex in the M2 brane action. We find that for $k>2$ the the quartic vertex contribution is cancelled by the Jacobian contribution for the choice of the separation of the fermionic zero modes from the quantum fields under which these form separate supermultiplets. Assuming the supersymmetric prescription for the paired zero modes we show that the cancellation persists after integration over the collective coordinates. Thus the ${\rm T}^{-1}_2$ correction vanishes, in agreement with the grand-canonical ensemble prediction. For $k=1$ the quartic vertex contribution reduces to equation-of-motion terms as in the case of ${\rm AdS}_3 \subset { \rm AdS}_7 \times S^4$ in arXiv:2511.22306 which is related to $S^3 \subset {\rm AdS}_4 \times S^7$ case by a formal analytic continuation.
Comments51 pages. v2,v3: added discussion of integration over the collective coordinates with the result about vanishing of the inverse tension correction confirmed, changes in section 1, new section 6 and appendix F
