中心扭曲的格里博夫谱与精细格里博夫-兹万齐格框架中的有限体积高斯响应
Center-twisted Gribov spectra and the finite-volume Gaussian response in the refined Gribov--Zwanziger framework
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中文总结 AI 辅助
该研究建立连续统框架对比格里博夫-兹万齐格与中心涡旋的禁闭描述，推导相关谱、核的有限体积性质，发现高斯计算未确立中心涡旋凝聚判据，分离了全局归一化问题与全局扭曲和动力学涡旋。
中文摘要 AI 辅助
我们通过电$\boldsymbol{\text{Z}_N^{[1]}}$1-形式对称性的规范不变扭曲配分函数，建立了一个连续统框架，用于对比格里博夫-兹万齐格（Gribov--Zwanziger）与中心涡旋（center-vortex）对禁闭的描述。背景2-形式场$B$等价于环面上的' t Hooft扭曲，它标记一个全局部分，本身并非动力学中心涡旋。对于$T^4$上的最小不可约扭曲，我们推导了$\text{SU}(N)$的完整伴随动量格。扭曲谱恰好是扩大环面上的标量谱，其周期为$(L_1,L_2,NL_3,NL_4)$，且排除了普通环面子格。这在平坦代表处产生有限的法捷耶夫-波波夫（Faddeev--Popov）能隙，并将扭曲减未扭曲的谱迹简化为普通环面迹。对于精细格里博夫-兹万齐格（RGZ）核，泊松重求和给出带有通用中心扭曲投影子的精确有限体积贝塞尔函数缠绕和。我们在固定RGZ参数下，计算了有限维全局零模/稳定子归一化的高斯单圈积分。兹万齐格行列式抵消，而规范固定/鬼部分在$T^4$上留下通用无质量带撇行列式；未扭曲部分还包含常数胶子模。唯一未被局部二次海森矩阵确定的归一化是可约未扭曲与不可约扭曲平坦连接的相对零模/稳定子测度。我们还推导了RGZ定态方程的闭合有限体积源。大体积时，质量响应呈指数抑制，而无质量因子依赖于全局零模归一化。因此，高斯计算本身并未确立$Z[B]/Z[0]$的强中心涡旋凝聚判据，但它分离了剩余的全局归一化问题，并将全局扭曲与实际动力学涡旋区分开。
英文摘要
We develop a continuum framework for comparing the Gribov--Zwanziger and center-vortex descriptions of confinement through the gauge-invariant twisted partition function of the electric $\mathbb{Z}_N^{[1]}$ 1-form symmetry. A background 2-form field $B$, equivalently an 't~Hooft twist on a torus, labels a global sector and is not itself a dynamical center vortex. For a minimal irreducible twist on $T^4$, we derive the complete adjoint momentum lattice of $SU(N)$. The twisted spectrum is exactly the scalar spectrum on an enlarged torus with periods $(L_1,L_2,NL_3,NL_4)$ with the ordinary-torus sublattice removed. This yields a finite Faddeev--Popov gap at the flat representative and reduces twisted-minus-untwisted spectral traces to ordinary torus traces. For the refined Gribov--Zwanziger (RGZ) kernel, Poisson resummation gives an exact finite-volume Bessel-function winding sum with a universal center-twist projector. We evaluate the Gaussian one-loop integral at fixed RGZ parameters up to the finite-dimensional global zero-mode/stabilizer normalization. The Zwanziger determinants cancel, while the gauge-fixing/ghost sector leaves a universal massless primed determinant on $T^4$; the untwisted sector also contains constant gluon modes. The only normalization not fixed by the local quadratic Hessian is the relative zero-mode/stabilizer measure of the reducible untwisted and irreducibly twisted flat connections. We also derive closed finite-volume sources for the RGZ stationary equations. The massive response is exponentially suppressed at large volume, whereas the massless factor depends on the global zero-mode normalization. Thus the Gaussian calculation does not by itself establish the strong center-vortex-condensation criterion for $Z[B]/Z[0]$, but it isolates the remaining global normalization problem and separates a global twist from an actual dynamical vortex.
发表机构
- Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（RIKEN跨学科理论与数学科学中心）
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