Nonperturbative Stabilization of D-Instantons in the Bosonic IIB Matrix Model
Abstract
We study the bosonic type IIB (IKKT) matrix model and the fate of the D-instanton positions p(i)μ, the diagonal components of the d Hermitian matrices, whose one-loop effective potential infamously drives them to a single point. We show that this collapse is an artifact of the leading (one-loop) truncation, while the actual non-collapse of the p(i)μ is a nonperturbative effect: it is invisible at one loop but already present in the exact (all-loop) two-body interaction. Since the two-body sector of the N× N model factorizes into copies of N=2, this interaction is captured exactly by the U(2) model, and we find that the two D-instantons do not collapse onto each other. To set up the computation, we gauge-fix the U(N) symmetry in a way that keeps the diagonal and off-diagonal sectors distinct, and we handle the residual U(1)N symmetry with an auxiliary-ghost BRST construction. This construction generates a new ghost four-leg vertex; the resulting Faddeev-Popov determinant admits a systematic large-separation expansion that organizes the effective potential into a many-body decomposition, separating the interaction into two-body, three-body, and higher-body contributions. The exact N=2 partition function is finite at finite separation; its naive Lorenz-gauge form develops a negative region at separations of order one, which we trace to a Gribov ambiguity of the Lorenz gauge and resolve with the maximal diagonal gauge--the classical frame containing the perturbative vacuum--where the short-distance force is finite and repulsive, so that the two-body potential develops a stable minimum at finite separation. These results are consistent with a stable, non-collapsed distribution of the p(i)μ; establishing the detailed distribution and full N-body non-collapse requires the higher-body potentials and is left to future work.
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BibTeX
@misc{chen2026nonperturbative,
title = {{Nonperturbative Stabilization of D-Instantons in the Bosonic IIB Matrix Model}},
author = {Yu-An Chen and Hikaru Kawai and Henry Liao and Cheng-Tsung Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.09598},
eprint = {2608.09598},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.09598},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonperturbative Stabilization of D-Instantons in the Bosonic IIB Matrix Model
AU - Yu-An Chen
AU - Hikaru Kawai
AU - Henry Liao
AU - Cheng-Tsung Wang
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2608.09598
UR - https://arxiv.org/abs/2608.09598
AB - We study the bosonic type IIB (IKKT) matrix model and the fate of the D-instanton positions p^(i)_μ, the diagonal components of the d Hermitian matrices, whose one-loop effective potential infamously drives them to a single point. We show that this collapse is an artifact of the leading (one-loop) truncation, while the actual non-collapse of the p^(i)_μ is a nonperturbative effect: it is invisible at one loop but already present in the exact (all-loop) two-body interaction. Since the two-body sector of the N× N model factorizes into copies of N=2, this interaction is captured exactly by the U(2) model, and we find that the two D-instantons do not collapse onto each other. To set up the computation, we gauge-fix the U(N) symmetry in a way that keeps the diagonal and off-diagonal sectors distinct, and we handle the residual U(1)^N symmetry with an auxiliary-ghost BRST construction. This construction generates a new ghost four-leg vertex; the resulting Faddeev-Popov determinant admits a systematic large-separation expansion that organizes the effective potential into a many-body decomposition, separating the interaction into two-body, three-body, and higher-body contributions. The exact N=2 partition function is finite at finite separation; its naive Lorenz-gauge form develops a negative region at separations of order one, which we trace to a Gribov ambiguity of the Lorenz gauge and resolve with the maximal diagonal gauge--the classical frame containing the perturbative vacuum--where the short-distance force is finite and repulsive, so that the two-body potential develops a stable minimum at finite separation. These results are consistent with a stable, non-collapsed distribution of the p^(i)_μ; establishing the detailed distribution and full N-body non-collapse requires the higher-body potentials and is left to future work.
ER -