Year: 2026
Type: preprint
Abstract: We compute the finite-$N$ Witten index of BMN matrix quantum mechanics after summing over all partition-labeled supersymmetric vacuum sectors. Starting from the unitary-matrix integral for each sector, we adapt two complementary evaluation methods to the BMN index: a symmetric-group character expansion, which reduces each fixed fugacity order to a finite combinatorial sum, and a residue expansion in which the contributing poles are organized by rooted trees, with a colored-tree generalization for multi-partition sectors. Where practical, direct integration and extraction of the constant term in the expanded integrand give independent coefficient-by-coefficient checks. We evaluate every vacuum sector for $N\leq 9$. In the equal-fugacity expansion, the coefficients near charges $j\sim N^2$ exhibit substantial cancellations between vacuum sectors, which tend to reduce the effective $N^2$ coefficient of the total index entropy. The finite-$N$ data also reveal a nontrivial sectoral organization: near $j=N^2$, the sector giving the largest contribution changes with $N$, from single-partition sectors at small rank to double-partition sectors starting at $N=6$. We call this phenomenon dominance switching. These results provide quantitative finite-$N$ input for using the BMN index as a diagnostic of protected plane-wave black-hole sectors and suggest in the controlled type-IIA regime a possible D2 dressed black-hole interpretation in which D0 black-hole sectors are accompanied by macroscopic spherical D2-brane degrees of freedom, analogous to dual dressed black holes in $AdS_5\times S^5$.
Source: arXiv (Cornell University)
Authors: Chang, Chi-Ming, Duary, Sarthak, Liu, Kangning
Institution: Tsinghua University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G4146574254, G7276017222, G7940611361
OpenAlex ID: W7162456713