Free energy dependence on spatial geometry for (2 + 1)-dimensional QFTs
Free energy dependence on spatial geometry for (2 + 1)-dimensional QFTs
复制标题
(2 1) 维 QFT 的自由能对空间几何的依赖性
DOI：
10.1088/1361-6382/ab353d
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发表时间：
2019
影响因子：
3.5
通讯作者：
Cheamsawat K
中科院分区：
文献类型：
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作者：
Cheamsawat K
我们考虑有限温度下的 (2+ 1)-QFT 与静态空间几何的时间乘积。适当定义的 QFT 在平坦空间变形上的热真空自由能与其在平坦空间上的值的差值是 UV 有限量，并且对于变形的合理衰减条件也是 IR 有限量。对于平坦空间的扰动，我们表明该自由能差与扰动幅度呈二次方关系，并且可以根据应力张量的线性响应来计算。作为说明，我们针对全息 CFT 进行了计算，发现在任何温度、任何扰动下，自由能都会减少。之前在自由标量和费米子以及零温度下的酉 CFT 中也发现了类似的行为，这表明 (2+1)-QFT 通常可能在很大程度上有利于褶皱的空间几何形状。我们还以相对于热尺度的静水小曲率膨胀来处理变形。然后，自由能变化由应力张量的曲率校正确定，并且对于这些理论，对于平坦空间的小曲率变形是负的。
We consider (2+ 1)-QFT at finite temperature on a product of time with a static spatial geometry. The suitably defined difference of thermal vacuum free energy for the QFT on a deformation of flat space from its value on flat space is a UV finite quantity, and for reasonable fall-off conditions on the deformation is IR finite too. For perturbations of flat space we show this free energy difference goes quadratically with perturbation amplitude and may be computed from the linear response of the stress tensor. As an illustration we compute it for a holographic CFT finding that at any temperature, and for any perturbation, the free energy decreases. Similar behaviour was previously found for free scalars and fermions, and for unitary CFTs at zero temperature, suggesting (2+ 1)-QFT may generally energetically favour a crumpled spatial geometry. We also treat the deformation in a hydrostatic small curvature expansion relative to the thermal scale. Then the free energy variation is determined by a curvature correction to the stress tensor and for these theories is negative for small curvature deformations of flat space.