Mapping AdS4 quantum gravity via the Bethe Ansatz formula
Abstract
The topologically twisted index of 3d ADHM theory can be written as a sum over solutions to the Bethe Ansatz Equations (BAEs) of the XXZ-type model constructed from quantum toroidal gl1. Via a novel numerical algorithm, we solve for all p(N) physical solutions at N≤ 21, where p(N) denotes the number of integer partitions of N. Surveying these solutions, we find that in addition to the known "1-cut" solution dual to dyonic black holes, where the gauge holonomies are distributed along a single curve in the complex plane, there are "dressed" 1-cut solutions dual to combined configurations of the black hole and M2-branes, m-cut solutions dual to ℤm orbifolds of the black hole, a discrete family of solutions interpolating between the 1-cut and 3-cut solutions, together with other exotic solutions, at each value of N. The free energy of the interpolating solutions cannot be matched with the on-shell action of any known bulk solution. The $1,2,3$-cut solutions and interpolating solutions all have a well-defined large N limit, and their leading order distribution of gauge holonomies can be computed analytically. Whenever possible, we fit the contributions of the solutions to the index to all orders in the 1/N expansion with high-precision numerics, and extract the leading non-perturbative correction. With exceptions, these are matched with the results of equivariant localization in the bulk, and the action of wrapped M2-branes respectively.
Related
- Generalized Coordinate Bethe Ansatz and Quantum Integrability of the Time-Dependent Massive Thirring Model
- On the commuting charges and the Bethe ansatz for the quantised Kadomtsev-Petviashvili equation
- Thermodynamic Bethe Ansatz for the Toda chain from inverse scattering transform
- The Gaudin model and the super Bethe ansatz for unitarizable modules over the general linear Lie (super)algebra
- Bethe ansatz without nesting
BibTeX
@misc{peng2026mapping,
title = {{Mapping AdS$_4$ quantum gravity via the Bethe Ansatz formula}},
author = {Cheng Peng and Xuao Zhang and Ziruo Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27097},
eprint = {2610.27097},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27097},
}
RIS
TY - UNPB
TI - Mapping AdS_4 quantum gravity via the Bethe Ansatz formula
AU - Cheng Peng
AU - Xuao Zhang
AU - Ziruo Zhang
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27097
UR - https://arxiv.org/abs/2610.27097
AB - The topologically twisted index of 3d ADHM theory can be written as a sum over solutions to the Bethe Ansatz Equations (BAEs) of the XXZ-type model constructed from quantum toroidal gl_1. Via a novel numerical algorithm, we solve for all p(N) physical solutions at N≤ 21, where p(N) denotes the number of integer partitions of N. Surveying these solutions, we find that in addition to the known "1-cut" solution dual to dyonic black holes, where the gauge holonomies are distributed along a single curve in the complex plane, there are "dressed" 1-cut solutions dual to combined configurations of the black hole and M2-branes, m-cut solutions dual to ℤ_m orbifolds of the black hole, a discrete family of solutions interpolating between the 1-cut and 3-cut solutions, together with other exotic solutions, at each value of N. The free energy of the interpolating solutions cannot be matched with the on-shell action of any known bulk solution. The $1,2,3$-cut solutions and interpolating solutions all have a well-defined large N limit, and their leading order distribution of gauge holonomies can be computed analytically. Whenever possible, we fit the contributions of the solutions to the index to all orders in the 1/N expansion with high-precision numerics, and extract the leading non-perturbative correction. With exceptions, these are matched with the results of equivariant localization in the bulk, and the action of wrapped M2-branes respectively.
ER -