Constant Maps and Exponentially Small Sectors in ABJM Bethe Observables
Abstract
The topologically twisted index of ABJM theory captures the microscopic entropy of magnetically charged supersymmetric AdS4 black holes. Building on the companion Letter arXiv:2608.04107, which reconstructed the finite-rank twisted superpotential at the universal twist, we determine the finite-rank index using high-precision Bethe-vacuum data, physics-informed symbolic regression, and integer relations. The Hessian, effective dilaton, and one-loop factors encode information beyond the on-shell twisted superpotential. The two observables share the same shifted rank. Within a declared finite class, we reconstruct the index constant map from the ABJM S3 constant maps at levels k and k/2, the constant map of the twisted superpotential, and elementary terms. We prove that it equals a convergent one-kernel integral for real k>0, resumming the large-k expansion, fixing a previously numerical constant, and yielding type-IIA coefficients at arbitrary genus. We also prove that the Clausen expression in arXiv:2608.04107 equals an alternating Euler sum and an absolutely convergent integral, giving closed evaluations for two rational-argument Euler-sum families. At k=1,2,4, the exponentially suppressed sectors exhibit arithmetic structure. The reconstructed coefficients of the twisted superpotential obey a divisor-sum formula with a conjectural all-order Eichler-integral series associated with a weight-four Eisenstein form. The index coefficients reduce to two rational generators; one admits modular-product formulas reproducing every available coefficient and suggesting an all-order completion. Conditional on this continuation, modular transformations determine the nearest logarithmic singularity, radius of convergence, and leading coefficient growth. These results provide a finite-N benchmark for quantum gravitational blocks and bulk black hole quantum entropy.
Related
- Continuous-time quantum control across an exponentially small bottleneck in a frustrated Ising ring model
- Constant-time equilibration of observables under rapid Lindbladian dynamics
- Exponentially long evaporation of noncommutative black hole
- Bethe-ansatz study of the Bose-Fermi mixture
- Chiral quantum chaos around exponentially many zero modes in the quantum breakdown model
BibTeX
@misc{hosseini2026constant,
title = {{Constant Maps and Exponentially Small Sectors in ABJM Bethe Observables}},
author = {Seyed Morteza Hosseini},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09273},
eprint = {2609.09273},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09273},
}
RIS
TY - UNPB
TI - Constant Maps and Exponentially Small Sectors in ABJM Bethe Observables
AU - Seyed Morteza Hosseini
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09273
UR - https://arxiv.org/abs/2609.09273
AB - The topologically twisted index of ABJM theory captures the microscopic entropy of magnetically charged supersymmetric AdS_4 black holes. Building on the companion Letter arXiv:2608.04107, which reconstructed the finite-rank twisted superpotential at the universal twist, we determine the finite-rank index using high-precision Bethe-vacuum data, physics-informed symbolic regression, and integer relations. The Hessian, effective dilaton, and one-loop factors encode information beyond the on-shell twisted superpotential. The two observables share the same shifted rank. Within a declared finite class, we reconstruct the index constant map from the ABJM S^3 constant maps at levels k and k/2, the constant map of the twisted superpotential, and elementary terms. We prove that it equals a convergent one-kernel integral for real k>0, resumming the large-k expansion, fixing a previously numerical constant, and yielding type-IIA coefficients at arbitrary genus. We also prove that the Clausen expression in arXiv:2608.04107 equals an alternating Euler sum and an absolutely convergent integral, giving closed evaluations for two rational-argument Euler-sum families. At k=1,2,4, the exponentially suppressed sectors exhibit arithmetic structure. The reconstructed coefficients of the twisted superpotential obey a divisor-sum formula with a conjectural all-order Eichler-integral series associated with a weight-four Eisenstein form. The index coefficients reduce to two rational generators; one admits modular-product formulas reproducing every available coefficient and suggesting an all-order completion. Conditional on this continuation, modular transformations determine the nearest logarithmic singularity, radius of convergence, and leading coefficient growth. These results provide a finite-N benchmark for quantum gravitational blocks and bulk black hole quantum entropy.
ER -