三维Lovelock引力与全息c-定理：全阶证明与重求和
3d Lovelock gravity and the holographic c-theorem: Proof at all orders and resummation
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中文总结 AI 辅助
本文证明了三维Lovelock引力在所有阶和任意耦合下满足全息c-定理，并给出了重求和形式的拉格朗日量、c-函数和中心电荷，其核心贡献是建立了尺度不变但非共形的对偶理论。
中文摘要 AI 辅助
我们证明了三维Lovelock引力，即由三维中的正则化Lovelock不变量得到的Horndeski理论，在所有阶和任意耦合值下都满足全息c-定理。在畴壁解的迷你超空间中，Horndeski标量方程在每一阶都是全导数，这在我们考虑的流中将标量的导数锁定为翘曲因子的导数，并允许将零能量条件积分成单调的c-函数。由此得到的真空的线性标量轮廓破坏了特殊共形变换，因此对偶理论是尺度不变的但不是共形的，中心电荷被定义为球面上on-shell作用量的对数发散系数。我们在Gauss-Bonnet情形下精确计算了它，并在完整塔下渐近计算了它，发现它关于耦合是线性的，并且与c-函数的UV值匹配。由于所有结果仅通过两个生成函数依赖于耦合，我们给出了导致正则黑洞的耦合选择下的重求和拉格朗日量、c-函数和中心电荷的闭式形式，并根据真空上有效牛顿常数的正性和具有非平凡标量的真空的唯一性对重求和理论进行了分类。
英文摘要
We prove that 3d Lovelock gravity, the Horndeski theory obtained from the regularized Lovelock invariants in three dimensions, admits a holographic c-theorem at all orders and for arbitrary values of the couplings. In the minisuperspace of domain wall solutions, the equation of the Horndeski scalar is a total derivative at every order, which locks the derivative of the scalar to that of the warp factor along the flows we consider and allows the null energy condition to be integrated into a monotonic c-function. The linear scalar profile of the resulting vacuum breaks the special conformal transformations, so the dual theory is scale-invariant but not conformal, and the central charge is defined as the coefficient of the logarithmic divergence of the on-shell action on the sphere. We compute it exactly for the Gauss-Bonnet case and asymptotically for the full tower, and find that it is linear in the couplings and matches the UV value of the c-function. Since all results depend on the couplings only through two generating functions, we give the resummed Lagrangians, c-functions and central charges in closed form for the choices of couplings that lead to regular black holes, and classify the resummed theories by the positivity of the effective Newton constant on the vacuum and the uniqueness of the vacuum with a non-trivial scalar.
发表机构
- Atılım University（阿提尔姆大学）
- Universidad de Las Américas, Sede Concepción（美洲大学孔塞普西翁校区）
- Sinop University（锡诺普大学）
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