AI 中文总结
该研究受有限截断全息术与广义$T\bar{T}$变形关系启发，在‘复杂度=任何事物’框架下，通过费弗曼 - 格雷厄姆展开推导广义复杂度修正，扩展了复杂度 - 体积提议，揭示了相关几何联系及非局部计算结构的出现。
AI 中文摘要
这项工作受有限截断全息术与广义$T\bar{T}$变形之间所提出关系的推动，在‘复杂度=任何事物’提议的框架内研究全息复杂度。利用有限截断表面附近的费弗曼 - 格雷厄姆展开，推导出变形对广义复杂度的修正，并表明其允许根据广义威尔莫尔型泛函进行系统展开。所得公式扩展了复杂度 - 体积提议的早期发现，涵盖任意几何复杂度度量。此外，修正结构可自然解释为多味洛伦兹线，不同线扇区对应复杂度泛函中的不同曲率不变量。这些结果展示了有限截断全息术、广义复杂度以及全息量子场论中非局部计算结构出现之间的几何联系。
英文摘要
This work is motivated by the proposed relationship among finite cut-off holography and generalized $T\bar T$ deformations, and examines holographic complexity within the framework of the "complexity = anything" proposal. Employing a Fefferman-Graham expansion near the finite cut-off surface, the deformation-induced correction to generalized complexity is derived and shown to allow a systematic expansion in terms of generalized Willmore-type functionals. The resulting formulation broadens earlier findings for the complexity-volume proposal to encompass arbitrary geometric complexity measures. Furthermore, the structure of the correction allows a natural interpretation as multiple-flavor Lorentzian threads, where distinct thread sectors correspond to different curvature invariants in the complexity functional. These results show a geometric connection among finite cut-off holography, generalized complexity, and the emergence of non-local computational structures in holographic quantum field theories.
Comments20 pages, 3 figures
