发表机构
National Taiwan University; Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University; Department of Physics, National Sun Yat-Sen University; KEK Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization; Graduate Institute for Advanced Studies, SOKENDAI（国立台湾大学; 大阪公立大学南村亮郎理论实验物理研究所(NITEP); 国立中山大学物理系; 高能加速器研究机构粒子核研究所学部理论中心; SOKENDAI高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对玻色型IIB矩阵模型中D瞬子位置因单圈有效势坍缩的问题，研究通过非微扰两体相互作用分析、规范固定与BRST构造，证明两体势在有限间距处存在稳定极小值，支持D瞬子的非坍缩分布。
AI 中文摘要
我们研究了玻色型IIB（IKKT）矩阵模型以及D瞬子位置$p^{(i)}_μ$（即$d$个厄米矩阵的对角分量）的演化行为——众所周知，其单圈有效势会驱使这些位置坍缩至单点。我们提出，这种坍缩是领头阶（单圈）截断的人为产物，而$p^{(i)}_μ$实际不会坍缩是一种非微扰效应：它在单圈阶不可见，但已存在于精确的（全圈）两体相互作用中。由于$N\times N$模型的两体扇区可分解为多个$N=2$的副本，该相互作用可通过$\text{U}(2)$模型精确捕获，我们发现两个D瞬子不会相互坍缩。为搭建计算框架，我们以保持对角与非对角扇区区分的方式对$\text{U}(N)$对称性进行规范固定，并通过辅助鬼场BRST构造处理剩余的$\text{U}(1)^N$对称性。该构造产生了新的四腿鬼顶点；所得的Faddeev-Popov行列式可进行系统的大间距展开，将有效势组织为多体分解形式，把相互作用拆分为两体、三体及更高体贡献。精确的$N=2$配分函数在有限间距下是有限的；其朴素的洛伦兹规范形式在量级为1的间距处会出现负区域，我们将其归因于洛伦兹规范的Gribov歧义，并通过最大对角规范（包含微扰真空的经典标架）予以解决——在该规范下，短程力是有限且排斥的，因此两体势在有限间距处形成稳定极小值。这些结果与$p^{(i)}_μ$的稳定、非坍缩分布相一致；确定其详细分布及完整$N$体非坍缩特性需要更高体势的研究，这留待未来工作开展。
英文摘要
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.
Comments41 pages, 5 figures; v2: minor modifications, references added
