M2 膜在 AdS$_4\times S^7/\mathbb Z_k$ 中：ABJM 理论中 $\frac{1}{2}$-BPS 威尔逊环的 2 圈修正与局域化
M2 brane in AdS$_4\times S^7/\mathbb Z_k$: 2-loop correction to $\frac{1}{2}$-BPS Wilson loop vs localization in ABJM theory
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中文总结 AI 辅助
该研究计算了 ABJM 理论中 M2 膜对偶的 1/2-BPS 威尔逊环的两圈修正，发现其在特定边界条件下为零，支持了巨正则系综匹配的提议。
中文摘要 AI 辅助
我们研究了包裹在 $\mathrm{AdS}_4\times S^7/\mathbb{Z}_k$ 内部 $\mathrm{AdS}_2\times S^1$ 上的 M2 膜的量子化，该膜与 ABJM 理论中的 $\frac{1}{2}$-BPS 圆形威尔逊环对偶。此前已证明经典作用和单圈贡献能够重现规范理论局域化结果。在此，我们将分析扩展到两圈阶。在自适应的静态和 $\kappa$-对称规范下，世界体积作用量不包含三次相互作用顶点，因此两圈修正完全由四次相互作用决定，并且明显没有对数紫外发散。我们发现玻色子和费米子贡献组合成一个完全平方 ${\mathscr X}^2$，其中 ${\mathscr X}$ 是玻色子和费米子三维格林函数及其导数的线性组合。$\mathscr X$ 的求值需要固定无质量费米子模式的 $\mathrm{AdS}_2$ 边界量子化。在由保留的超对称性所选择的边界条件下，$\mathscr X$ 为零，因此发现完整的两圈修正为零。这个结果与将 M2 膜圈展开直接等同于规范固定 $(N,k)$ 局域化预言的大 $N$ 展开不一致。相反，它精确地符合最近的提议，即半经典 M2 膜配分函数应与规范理论巨正则系综匹配，在该系综中威尔逊环期望值在微扰意义上是单圈精确的。因此，两圈修正的消失为这种巨正则识别提供了非平凡的检验。
英文摘要
We study the quantization of an M2 brane wrapping $\mathrm{AdS}_2\times S^1$ inside $\mathrm{AdS}_4\times S^7/\mathbb{Z}_k$, dual to the $\frac{1}{2}$-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 ${\mathscr X}$ is a linear combination of the bosonic and fermionic 3d Green's functions and their derivatives. The evaluation of $\mathscr X$ requires fixing the $\mathrm{AdS}_2$ boundary quantization of the massless fermionic modes. With the boundary conditions selected by the preserved supersymmetry, $\mathscr X$ 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.
发表机构
- Università del Salento（萨伦托大学）
- INFN - sezione di Lecce（意大利国家核物理研究所莱切分部）
- Abdus Salam Centre for Theoretical Physics, Imperial College London（伦敦帝国理工学院阿卜杜斯·萨拉姆理论物理中心）
- ITMP of MSU（莫斯科国立大学理论与数学物理研究所）
- Lebedev Inst.（列别捷夫研究所）
机构由 AI 辅助整理，请以论文原文为准。
