平面波极限下的ABJM/BMN指标匹配

中文摘要 AI 辅助

我们在平面波极限下，对任意固定的正Chern-Simons能级k，建立了ABJM理论与BMN矩阵模型的细化超对称指标之间的逐系数相等性。对于具有固定重数（从而具有固定有限ABJM规范秩）的多膜族，当所有纵向动量趋于无穷大且其两两差值固定时，该相等性成立。标量修饰的等通量ABJM磁单极子对应于模糊球面膜的BMN真空：重数计数重合的膜，而通量大小给出沿M理论圆的每膜动量。在指标层面，相关的Higgs留数产生ABJM平面波贡献的对角规范场积分，其磁单极子谐波核与BMN矩阵谐波核一致，直至有限的BMN上自旋截断。在有限动量下，完整指标差分解为非平面波余项和该截断以上的谐波尾部。增大k将前者移至更高的荷级，而不改变存留的核或截断贡献。这给出了早期单膜指标关系的逐系数、多膜推广。

英文摘要

We establish coefficientwise equality between the refined supersymmetric indices of ABJM theory and the BMN matrix model in the plane-wave limit at every fixed positive Chern-Simons level k. For multi-membrane families with fixed multiplicities, and hence fixed finite ABJM gauge rank, the equality holds as all longitudinal momenta tend to infinity with their pairwise differences fixed. Scalar-dressed equal-flux ABJM monopoles correspond to BMN vacua of fuzzy-sphere membranes: multiplicities count coincident membranes, whereas flux magnitudes give the momentum per membrane along the M-theory circle. At the index level, the associated Higgs residues yield a diagonal-holonomy integral for the ABJM plane-wave contribution, whose monopole-harmonic kernel agrees with the BMN matrix-harmonic kernel up to the finite BMN upper-spin cutoff. At finite momentum, the full index difference splits into the non-plane-wave remainder and the harmonic tail above this cutoff. Increasing k shifts the former to higher fugacity grade without changing the surviving kernel or the cutoff contribution. This gives a coefficientwise, multi-membrane extension of the earlier single-membrane index relation.

发表机构

• Yau Mathematical Sciences Center (YMSC), Tsinghua University（清华大学丘成桐数学科学中心）
• Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京国际数学研究中心）
• Peng Huanwu Center for Fundamental Theory（彭桓武理论物理中心）
• Department of Mathematical Sciences, Tsinghua University（清华大学数学科学系）
• Jefferson Physical Laboratory, Harvard University（哈佛大学杰斐逊物理实验室）

机构由 AI 辅助整理，请以论文原文为准。

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5 pages + supplement