Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM

Ji-Seong Chae

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arXiv · 2608.01349

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM

Ji-Seong Chae

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Abstract

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.

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Ji-Seong Chae. 2026-08-02. Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM. https://arxiv.org/abs/2608.01349

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