发表机构
Peaceful Society, Science and Innovation Foundation; Department of Occupational Science & Occupational Therapy, Faculty of Medicine, University of British Columbia; Faculty of Land and Food Systems, University of British Columbia（和平社会科学与创新基金会; 不列颠哥伦比亚大学医学院职业科学与职业治疗系; 不列颠哥伦比亚大学土地与食品系统学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出经典时空是USMEG-EFT中的引力凝聚体，通过量子修正鞍点方程确定凝聚解体标度，解决了Verlinde熵引力的不一致性。
AI 中文摘要
我们提出一个推导，表明在统一标准模型与涌现引力-有效场论（USMEG-EFT）框架内，经典时空几何是一种“引力凝聚体”：背景度规 $\barg_{\mu\nu}$ 是量子度规算符的真空期望值，作为引力破缺标度 $\Lgrav \sim 10^{18}$ GeV 以下的有序相存在。凝聚相的特征是非简并度规期望值，这是一个微分同胚不变判据，其受控实现被限制在 $\Lgrav$ 以下的标度。框架内的三个收敛的量子场论分析，即正则协变破缺 \cite{Chishtie23}、单圈重整化群分析 \cite{Chishtie25CJP} 和条件BRST闭合 \cite{ChishtieSymmetry26}，将该标度识别为受控几何描述的边界。我们证明，通过拉格朗日乘子路径积分的Legendre变换定义的凝聚序参量 \cite{BrandtFrenkelMcKeon20,McKeonBrandt25} 满足一个量子修正的鞍点方程，其单圈修正项在 $\Lgrav$ 处增长到树级项的大小，超过该标度框架不再提供受控的非简并解；我们将此边界解释为凝聚体解体的开始。由于拉格朗日乘子约束作用于虚引力子涨落，并恰好在一圈处终止引力扇区，该边界源于一个有限且闭合的量子修正集合，这与广义相对论标准有效场论处理中导数展开的逐渐失效形成对比 \cite{Donoghue94}。该机制从根本上不同于Verlinde的熵引力方案，并解决了其已知的不一致性。
英文摘要
We present a derivation showing that classical spacetime geometry is a \emph{gravitational condensate} within the Unified Standard Model with Emergent Gravity--Effective Field Theory (USMEG-EFT): the background metric $\barg_{μν}$ is the vacuum expectation value of the quantum metric operator, existing as an ordered phase below the gravitational breakdown scale $\Lgrav \sim 10^{18}$\,GeV. The condensed phase is characterized by a nondegenerate metric expectation value, a diffeomorphism-invariant criterion whose controlled realization is confined to scales below $\Lgrav$. Three convergent quantum-field-theoretic analyses within the framework, namely canonical covariance breakdown \cite{Chishtie23}, one-loop renormalization group analysis \cite{Chishtie25CJP}, and conditional BRST closure \cite{ChishtieSymmetry26}, identify this scale as the boundary of the controlled geometric description. We show that the condensate order parameter, defined via the Legendre transform of the Lagrange multiplier path integral \cite{BrandtFrenkelMcKeon20,McKeonBrandt25}, satisfies a quantum-corrected saddle-point equation whose one-loop correction grows to the size of the tree term at $\Lgrav$, beyond which the framework supplies no controlled nondegenerate solution; we interpret this boundary as the onset of condensate dissolution. Because the Lagrange multiplier constraint acts on virtual graviton fluctuations and terminates the gravitational sector exactly at one loop, this boundary arises from a finite, closed set of quantum corrections, in contrast to the gradual failure of the derivative expansion in the standard effective field theory treatment of general relativity \cite{Donoghue94}. This mechanism is fundamentally distinct from, and resolves known inconsistencies of, Verlinde's entropic gravity programme.
Comments8 pages, published version at Physics Letters B
Journal refPhysics Letters B, Vol. 880, 140803, 2026
DOI：10.1016/j.physletb.2026.140803
