谱分数玻色弦：精确Polyakov测度与临界维度
Spectral Fractional Bosonic Strings: Exact Polyakov Measure and the Critical Dimension
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中文总结 AI 辅助
该论文将分数拉普拉斯算子置于动态世界面上，通过交织算子与zeta雅可比行列式推导出精确Polyakov测度，确定临界维度为26/s，并证明整数临界轨迹上残余行列式对应局域临界CFT，从而将分数指数转化为量子几何一致性参数。
中文摘要 AI 辅助
分数拉普拉斯算子编码了量子物质和全息边界系统中的反常标度与协变非局域响应。我们将相应的标量谱理论置于动态闭合世界面上。一个依赖于度量的交织算子将分数二次型映射为$D$个自由玻色子的二次型，而其zeta雅可比行列式将物质行列式权重从$D$改变为$sD$。素数行列式变换包含零模面积因子，并同时决定模密度和Weyl系数$c_{\rm det}=sD$。因此，Weyl抵消选择$D_\ast=26/s$。在整数临界轨迹$1\leq D\leq26$上，$N=26-D$个旁观玻色子将剩余行列式转化为局域临界共形场论。其固定面积亏格$g$真空测度为26个自由玻色子的测度，其环面迹是模不变的，其管道通道是态分辨的，且其BRST荷是幂零的。$D$个区分坐标仍为谱复合体；它们的拉回产生Koba-Nielsen振幅和无质量顶点条件。耦合到该区分扇区的靶背景保留普通单圈张量beta函数，具有膨胀子亏损$sD-26$和相应的弦框架作用。因此，世界面引力将分数指数转化为量子几何一致性参数。
英文摘要
Fractional Laplacians encode anomalous scaling and covariant nonlocal response in quantum matter and holographic boundary systems. We place the corresponding scalar spectral theory on a dynamical closed worldsheet. A metric-dependent intertwiner maps the fractional quadratic form to that of $D$ free bosons, while its zeta Jacobian changes the matter determinant weight from $D$ to $sD$. The prime-determinant transformation includes the zero-mode area factor and determines both the moduli density and the Weyl coefficient $c_{\rm det}=sD$. Weyl cancellation therefore selects $D_\ast=26/s$. On the integer critical locus $1\leq D\leq26$, $N=26-D$ spectator bosons turn the residual determinant into a local critical CFT. Its fixed-area genus-$g$ vacuum measure is that of 26 free bosons, its torus trace is modular invariant, its plumbing channels are state resolved, and its BRST charge is nilpotent. The $D$ distinguished coordinates remain spectral composites; their pullback yields the Koba--Nielsen amplitudes and massless vertex conditions. Target backgrounds coupled to this distinguished sector retain the ordinary one-loop tensor beta functions, with dilaton deficit $sD-26$ and the corresponding string-frame action. Worldsheet gravity thus turns the fractional exponent into a quantum-geometric consistency parameter.
发表机构
- Department of Physics University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系）
机构由 AI 辅助整理，请以论文原文为准。
