AI 中文总结
针对五维弦导出的洛夫洛克-霍恩德斯基理论，构建了其渐近局域 AdS 分支的重整化生成泛函，证明全息响应可重构高维参数，为弦约化提供边界指纹。
AI 中文摘要
弦导出的高阶曲率标量-张量引力理论在边界响应中编码了微观耦合数据，这引发了一个问题：全息可观测量是否可以重构底层的高维参数。我们针对五维弦导出的洛夫洛克-霍恩德斯基（SDLH）理论，在其精确线性 dilaton 渐近局域 AdS 分支上回答了该问题，为任意边界度规和时空依赖的标量源构建了重整化生成泛函。边界协变径向层级统一了变分问题、局域反作用、对数障碍、有限单点函数以及沃德恒等式。两个响应行列式组织了递归、共振障碍以及度规-标量混合。Weyl 反常浓缩为欧拉密度、Weyl² 密度以及单个曲率-标量平方，其配对变分产生了度规和标量障碍。所得的重整化泛函将弦选定的耦合数据带入边界几何、算符响应、反常系数以及与引力可观测量的可计算接口。在正则分支上，四个标量归一化不变的全息组合对连续约化耦合具有全局有理逆映射。在固定紧致化维度下，该映射具有最大秩，而曲率-反常和可重构无符号歧义的高维高斯-博内系数。因此，全息响应为底层弦约化提供了一个明确的、超定的边界指纹。
英文摘要
String-derived higher-curvature scalar--tensor gravities encode microscopic coupling data in boundary response, raising the question of whether holographic observables can reconstruct the underlying higher-dimensional parameters. We answer this question for the five-dimensional string-derived Lovelock--Horndeski (SDLH) theory on its exact linear-dilaton asymptotically locally AdS branch, constructing the renormalized generating functional for an arbitrary boundary metric and spacetime-dependent scalar source. A boundary-covariant radial hierarchy unifies the variational problem, local backreaction, logarithmic obstruction, finite one-point functions, and Ward identities. Two response determinants organize the recursion, resonant obstructions, and metric--scalar mixing. The Weyl anomaly condenses into an Euler density, a Weyl-squared density, and a single curvature--scalar square whose paired variations generate the metric and scalar obstructions. The resulting renormalized functional carries string-selected coupling data into boundary geometry, operator response, anomaly coefficients, and a calculable interface with gravitational observables. On the regular branch, four scalar-normalization-invariant holographic combinations admit a global rational inverse to the continuous reduced couplings. At fixed compactification dimension the map has maximal rank, while the curvature-anomaly sum reconstructs the higher-dimensional Gauss--Bonnet coefficient without sign ambiguity. Holographic response thus provides an explicit, overdetermined boundary fingerprint of the underlying string reduction.
Comments29 pages
