Year: 2026
Type: preprint
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 $N\times N$ model factorizes into copies of $N=2$, this interaction is captured exactly by the $\mathrm{U}(2)$ model, and we find that the two D-instantons do not collapse onto each other. To set up the computation, we gauge-fix the $\text{U}(N)$ symmetry in a way that keeps the diagonal and off-diagonal sectors distinct, and we handle the residual $\mathrm{U}(1)^N$ 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.
Source: arXiv (Cornell University)
Authors: Chen, Yu-An, Kawai, Hikaru, Liao, Henry, Wang, Cheng-Tsung
Institutions: National Taiwan University, National Sun Yat-sen University, Osaka Metropolitan University, Nambu Yoichiro Institute of Theoretical and Experimental Physics, Osaka Metropolitan University, High Energy Accelerator Research Organization, The Graduate University for Advanced Studies, SOKENDAI, Institute of Particle and Nuclear Studies
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7202215744