热态中的反c函数
Inverted c-functions in thermal states
摘要：
我们首先通过全息术计算了强耦合下$\mathcal{N}=4$ Super-Yang-Mills理论中手征反常、电荷和磁场对纠缠熵的影响。根据纠缠带的宽度，纠缠熵探测器的能量从紫外到红外能量范围的量子场论（QFT）在一个给定的状态准备。从纠缠熵出发，计算了全息c函数，并证明了一个逆c定理。也就是说，这些c-函数在一般的热状态单调增加的红外（IR）的能量制度。这与真空态中的c函数相反，真空态中的c函数沿着重整化群流朝向可重整化QFT的IR区域减小。此外，在热态和IR极限中，c函数表现为热行为，与热熵的值成比例地增长。手性异常影响的c-功能更多的IR制度，其效果是在一个固定的化学势和温度的磁场的中间值达到峰值。
英文摘要：
We first compute the effect of a chiral anomaly, charge, and a magnetic field on the entanglement entropy in $\mathcal{N}=4$ Super-Yang-Mills theory at strong coupling via holography. Depending on the width of the entanglement strip the entanglement entropy probes energy scales from the ultraviolet to the infrared energy regime of this quantum field theory (QFT) prepared in a given state. From the entanglement entropy, we compute holographic c-functions and demonstrate an inverted c-theorem for them. That is, these c-functions in generic thermal states monotonically increase towards the infrared (IR) energy regime. This is in contrast to the c-functions in vacuum states which decrease along the renormalization group flow towards the IR regime of a renormalizable QFT. Furthermore, in thermal states and in the IR limit, the c-functions behave thermally, growing proportionally to the value of the thermal entropy. The chiral anomaly affects the c-functions more in the IR regime, and its effect is peaked at an intermediate value of the magnetic field at a fixed chemical potential and temperature.
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