标题： $\mathcal N=4$对称线缺陷Schur指标和半经典弦 显示英文标题

标题： $\mathcal N=4$ SYM line defect Schur index and semiclassical string

摘要： 四维$\mathcal N=4$ $U(N)$ SYM 中线缺陷 Schur 指数的巨引力子展开最近在 arXiv:2403.11543 中被提出，可以通过在对偶弦理论中计数两个半无限基本弦在$AdS_{5}\times S^{5}$上结束于线缺陷和 D3 膜巨引力子的涨落态来捕捉。 然而，为了与有限$N$的缺陷线指标的规范理论数据一致，需要包含来源不明的额外贡献。 我们通过在扭曲背景中对半经典弦划分函数的直接分析，讨论了缺陷线指标的巨引力子展开的大$N$领先阶贡献。 我们在存在 D3 膜的情况下讨论了超对称边界条件，并通过引入合适的涨落模式投影来评估二次涨落有效作用量。 我们表明，在 arXiv:2403.11543 中发现的单个巨引力子修正的额外贡献对应于超对称卡西米尔能量贡献。 显示英文摘要

摘要： The giant graviton expansion of the line defect Schur index in four dimensional $\mathcal N=4$ $U(N)$ SYM was recently proposed in arXiv:2403.11543 to be captured in the dual string theory by counting fluctuations states of two half-infinite fundamental strings in $AdS_{5}\times S^{5}$ ending on the line defect and D3 brane giant. However, agreement with the gauge theory data for the defect line index at finite $N$ required the inclusion of ad hoc extra contributions with unclear origin. We discuss the large $N$ leading order contribution of the giant graviton expansion of the defect line index by a direct analysis of semiclassical string partition function in a twisted background. We discuss supersymmetric boundary conditions in the presence of the D3 brane and evaluate the quadratic fluctuations effective action by introducing a suitable projection of fluctuation modes. We show that the extra contributions to the single giant graviton correction found in arXiv:2403.11543 correspond to a supersymmetric Casimir energy contribution.