arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2009.07040hep-th
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数值相对论、全息术和量子势能条件

Numerical Relativity, Holography and the Quantum Null Energy Condition

Philipp Stanzer

摘要:

量子零能条件(QNEC)是量子理论中唯一已知的自洽局域能量条件。与量子场论中被违反的经典能量条件相反,量子非牛顿效应是量子聚焦猜想的结果,并且已经在几种特殊情况下得到了证明,一般来说,在三个或更多的时空维度中的量子场论也是如此。QNEC涉及所考虑的理论的内在量子性质,即纠缠熵(EE)。虽然在QFT中EE是出了名的难以计算,但全息原理提供了一个简单的几何描述。一般来说,全息原理把没有引力的规范理论与更高一维的量子引力理论联系起来。全息术提供了一种方法来了解强耦合场论以及量子引力和调查QNEC在这方面无疑将导致新的见解。在这篇论文中,重点放在$2$ -和$4$ -维场论,在那里我们研究系统的日益复杂的数值和分析方法。在真空、热态、整体猝灭态和一个重离子碰撞模型中,我们发现QNEC总是满足的,有时是饱和的,但它可以比经典的零能条件更强或更弱。有趣的是,在二维中,QNEC $_2$在本体物质存在下不能饱和。一个大质量标量粒子的反反应提供了一个例子,其中有限的饱和间隙是精确已知的。考虑耦合到爱因斯坦引力的大质量自相互作用标量场导致从小黑洞到大黑洞的相变。对偶场理论为使用QNEC $_2$作为研究强耦合动力系统的工具提供了一个丰富的例子。特别是知道QNEC $_2$在基态,使我们能够作出声明的相结构的热状态。

英文摘要:

The quantum null energy condition (QNEC) is the only known consistent local energy condition in quantum theories. Contrary to the classical energy condition which are known to be violated in QFT, QNEC is a consequence of the quantum focussing conjecture and has been proven for several special cases and in general for QFTs in three or more spacetime dimensions. QNEC involves an intrinsically quantum property of the theory under consideration, the entanglement entropy (EE). While EE is notoriously hard to calculate in QFT, the holographic principle provides a simple geometric description. In general the holographic principle relates a gauge theory without gravity to a theory of quantum gravity in one dimension higher. Holography provides a way to learn about strongly coupled field theories as well as quantum gravity and investigating QNEC in this context will undoubtedly lead to new insights. In this thesis the focus is put on $2$- and $4$-dimensional field theories, where we study systems of increasing complexity with numerical and analytical methods. In vacuum, thermal states, globally quenched states and a toy model for heavy ion collisions we find that QNEC is always satisfied and sometimes saturated, while it can be a stronger or weaker condition than the classical null energy condition. Interestingly in two dimensions QNEC$_2$ cannot be saturated in the presence of bulk matter. The backreaction of a massive scalar particle provides an example where the finite gap to saturation is precisely known. Considering a massive self-interacting scalar field coupled to Einstein gravity leads to phase transitions from small to large black holes. The dual field theory provides a rich example to use QNEC$_2$ as a tool to learn about strongly coupled dynamical systems. In particular knowing QNEC$_2$ in the ground state allows us to make statements about the phase structure of the thermal states.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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