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

2026/08/02 by Ji-Seong Chae
Physics and Astronomy · #hep-th

paper · pdf

arxiv created 2026/08/02 · arxiv updated 2026/08/04

Abstract

We study the finite-N superconformal index of four-dimensional \mathcal N=4 U(N) Yang--Mills theory with antisymmetric elliptic Ruijsenaars--Schneider (eRS) insertions. The eRS insertions turn the uninserted index, which is an unweighted spectral sum, into a family of protected observables weighted by eRS eigenvalues and therefore retain finite-N information not determined by the ordinary index alone On the codimension-one locus t=q, p=uv, the eRS operators become conjugate to free shifts, allowing us to rewrite the self-glued index as a bilateral free-fermion determinant. This gives exact finite-N formulas for all antisymmetric ranks and makes the u↔ v structure manifest. On the boundary v=0, we determine the complete stable tower of pure u^kN defect-resolved corrections, while the bilateral two-charge formula captures the reflected v^kN sectors and mixed u--v contributions, including the first mixed giant-graviton sector. We also develop the expansion away from the solvable locus through second order. Finally, we reproduce the ordinary one-giant coefficient from a maximal-D3 determinant and identify the additional microscopic input required to complete the bulk derivation of the defect correction.

Citations

• Deformed Schur indices and Macdonald polynomials
• Analytic continuation and the giant graviton expansion
• Giant graviton expansion from eigenvalue instantons
• On Ruijsenaars-Schneider spectrum from superconformal indices and ramified instantons
• Giant graviton expansion for general Wilson line operator indices
• Schur line defect correlators and giant graviton expansion
• Giant graviton expansion of Schur index and quasimodular forms
• Holographic Tests for Giant Graviton Expansion
• Holographic tests for giant graviton expansion
• Simple-Sum Giant Graviton Expansions for Orbifolds and Orientifolds
• On the brane expansion of the Schur index
• Comments on the Giant-Graviton Expansion of the Superconformal Index
• Unitary matrix models, free fermion ensembles, and the giant graviton expansion
• The Giant Graviton Expansion
• Finite-N superconformal index via the AdS/CFT correspondence
• Kronecker theta function and a decomposition theorem for theta functions I
• Macdonald processes
• Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram