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arXiv 1606.02420hep-th
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负能态的全息描述

A Holographic Description of Negative Energy States

Da-Shin Lee, Chen-Pin Yeh

摘要:

利用AdS/CFT对偶性,研究了具有一般动力学标度$z$的$2+1$维量子临界理论中应力张量的期望值,探讨了强耦合场论中负能量密度的各种约束.全息对偶理论是3+1维Lifshitz背景下的引力理论。我们采用一致的方法从体结构得到边界应力张量,它满足与Lifshitz标度对称性相关的迹沃德恒等式。特别是,边界应力张量,构造从引力波变形Lifshitz几何,被发现到二阶的引力波扰动。{The结果}与同阶自由{标量}场论中的相应结果进行了比较。这使我们能够将引力波的边界值与压缩真空态的压缩参数联系起来。我们发现,在这两种情况下与$z=1$,应力张量满足平均零能量条件,是符合量子兴趣猜想。此外,零收缩应力张量的负下界,这是平均的类时轨迹沿近零方向,得到。与自由相对论场论相比,我们发现强耦合场论中对负零能量密度的大小和持续时间的约束较弱。的影响进行了讨论。

英文摘要:

Using the AdS/CFT duality, we study the expectation value of stress tensor in $2+1$-dimensional quantum critical theories with a general dynamical scaling $z$, and explore various constrains on negative energy density for strongly coupled field theories. The holographic dual theory is the theory of gravity in 3+1-dimensional Lifshitz backgrounds. We adopt a consistent approach to obtain the boundary stress tensor from bulk construction, which satisfies the trace Ward identity associated with Lifshitz scaling symmetry. In particular, the boundary stress tensor, constructed from the gravitational wave deformed Lifshitz geometry, is found up to second order in gravitational wave perturbations. {The result} is compared to its counterpart in free {scalar} field theory at the same order in an expansion of small squeezing parameters. This allows us to relate the boundary values of gravitational waves to the squeezing parameters of squeezed vacuum states. We find that, in both cases with $z=1$, the stress tensor satisfies the averaged null energy condition, and is consistent with the quantum interest conjecture. Moreover, the negative lower bound on null-contracted stress tensor, which is averaged over time-like trajectories along nearly null directions, is obtained. We find a weaker constraint on the magnitude and duration of negative null energy density in strongly coupled field theory as compared with the constraint in free relativistic field theory. The implications are discussed.

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