论文标题
对称2张及其引力双重的GJMS样运算符
GJMS-like operators on symmetric 2-tensors and their gravitational duals
论文作者
论文摘要
我们研究了一个高衍生的保形操作员的家族$ p_ {2k}^{（2）} $作用于通用爱因斯坦空间上的横向无跟踪对称2 tensor。它们是众所周知的标量结构的自然概括。 我们首先通过使用ADS/CFT字典来根据庞大的Poincaré-Einstein指标提供替代描述，并认为它们的全息双重双重偶发由大量的大型引力组成。在一环量子水平上，我们提出了一个全息公式，用于在具有标准和替代边界条件的大型重力元中的高源保形算子的功能决定因素$ p_ {2k}^{（2）} $。也制定了向量的类似构造$ p_ {2k}^{（1）} $，我们还通过将纵向部分解耦来重写无约束矢量的全息公式和无可怜的对称2 tensor。 最后，我们表明全息公式提供了必要的构件来解决无质量和部分无质量的散装重力。这在四个和六个维度中得到了证实，并与文献中可用的结果完全达成了共识。
We study a family of higher-derivative conformal operators $P_{2k}^{(2)}$ acting on transverse-traceless symmetric 2-tensors on generic Einstein spaces. They are a natural generalization of the well-known construction for scalars. We first provide the alternative description in terms of a bulk Poincaré-Einstein metric by making use of the AdS/CFT dictionary and argue that their holographic dual generically consists of bulk massive gravitons. At one-loop quantum level, we put forward a holographic formula for the functional determinant of the higher-derivative conformal operators $P_{2k}^{(2)}$ in terms of the functional determinant for massive gravitons with standard and alternate boundary conditions. The analogous construction for vectors $P_{2k}^{(1)}$ is worked out as well and we also rewrite the holographic formula for unconstrained vector and traceless symmetric 2-tensor by decoupling the longitudinal part. Finally, we show that the holographic formula provides the necessary building blocks to address the massless and partially massless bulk gravitons. This is confirmed in four and six dimensions, verifying full agreement with results available in the literature.
