$\boldsymbol{\textit{N}}$=4 SYM中精确的有限$\boldsymbol{N}$ eRS曲面缺陷指标与巨引力子修正
Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM
AI总结：
该研究针对带反对称eRS插入项的四维$\boldsymbol{\textit{N}}$=4 SYM，推导有限$\boldsymbol{N}$超共形指标的精确公式，分析缺陷修正与巨引力子贡献，确定可解轨迹外的二阶展开式及体推导的额外微观输入。
AI中文摘要：
我们研究四维$\boldsymbol{\textit{N}}$=4 $U(N)$杨-米尔斯理论的有限$\boldsymbol{N}$超共形指标，该理论带有反对称椭圆Ruijsenaars-Schneider（eRS）插入项。eRS插入项将无插入时的未加权谱和形式指标，转化为由eRS本征值加权的一系列受保护观测量，因此保留了普通指标单独无法确定的有限$\boldsymbol{N}$信息。在余维一轨迹$t=q$、$p=uv$上，eRS算子变为共轭自由平移，这使我们能将自胶合指标重写为双边自由费米子行列式，为所有反对称秩给出精确的有限$\boldsymbol{N}$公式，并显式呈现$u\boldsymbol{\rightarrow}v$结构。在边界$v=0$处，我们确定了纯$u^{kN}$缺陷分辨修正的完整稳定塔，而双边两荷公式捕获反射的$v^{kN}$扇区与混合$u-v$贡献，包括首个混合巨引力子扇区。我们还通过二阶项开发了可解轨迹外的展开式。最后，我们从极大D3行列式重现普通单巨系数，并确定完成缺陷修正的体推导所需的额外微观输入。
英文摘要：
We compute the exact finite-\(N\) superconformal index of four-dimensional \(\mathcal N=4\) \(U(N)\) Yang--Mills theory with antisymmetric elliptic Ruijsenaars--Schneider (eRS) surface-defect insertions. By matching the inserted eRS Hamiltonians to their independent realization in five-dimensional \(\mathcal N=1^*\) gauge theory, we interpret that the solvable locus \(t=q\) corresponds to vanishing adjoint mass. Motivated by this massless specialization, we impose the four-dimensional balancing condition \(p=uv\). At this point, the eRS operators are conjugate to free \(q\)-shifts, and the self-glued matrix integral reduces to a bilateral free-fermion determinant. This gives closed finite-\(N\) formulas for every antisymmetric rank. On \(v=0\), we determine the stable pure \(u^{kN}\) corrections at all wrapping orders; the bilateral formula also captures the reflected \(v^{kN}\) sectors and mixed \(u\)--\(v\) contributions. We further formulate the balanced perturbation away from \(t=q\) through second order in terms of connected correlators. Finally, a maximal-D3 determinant reproduces the ordinary one-giant coefficient and isolates the microscopic input required for the defect correction.
