超越米兰斯基缩放
Beyond Miransky Scaling
摘要：
我们研究了强味渐近自由规范理论中物理观测量的标度行为，如多味QCD。当费米子味的数量增加时，这种理论接近量子临界点。众所周知，在这个量子临界点的物理观测量表现出指数标度行为（米兰斯基标度），只要规范耦合被认为是一个常数的外部参数。当考虑到规范耦合的尺度依赖性时，这种标度行为被修改。只要规范耦合接近IR不动点，我们得到的普遍幂律修正的指数标度行为，并表明它们是唯一确定的规范耦合的IR临界指数。为了说明我们的发现，我们用非微扰泛函重整化群方法计算了多味QCD中的普适修正。在这种情况下，我们期望幂律标度在定量上更相关，如果理论被探测，例如，在整数Nf，如在晶格模拟中所做的那样。
英文摘要：
We study the scaling behavior of physical observables in strongly-flavored asymptotically free gauge theories, such as many-flavor QCD. Such theories approach a quantum critical point when the number of fermion flavors is increased. It is well-known that physical observables at this quantum critical point exhibit an exponential scaling behavior (Miransky scaling), provided the gauge coupling is considered as a constant external parameter. This scaling behavior is modified when the scale dependence of the gauge coupling is taken into account. Provided that the gauge coupling approaches an IR fixed point, we derive the resulting universal power-law corrections to the exponential scaling behavior and show that they are uniquely determined by the IR critical exponent of the gauge coupling. To illustrate our findings, we compute the universal corrections in many-flavor QCD with the aid of nonperturbative functional renormalization group methods. In this case, we expect the power-law scaling to be quantitatively more relevant if the theories are probed, for instance, at integer Nf as done in lattice simulations.
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