We show that four-dimensional systems may exhibit a topological phase transition analogous to the well-known Berezinskii-Kosterlitz-Thouless vortex unbinding transition in two-dimensional systems. We study a suitable generalization of the sine-Gordon model in four dimensions and the renormalization group flow equation of its couplings, showing that the critical value of the frequency is the square of the corresponding value in 2D. The value of the anomalous dimension at the critical point is determined ($\eta =1/32$) and a conjecture for the universal jump of the superfluid stiffness ($4/{\pi }^2$) presented.

中文翻译：

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四个维度的拓扑相变

我们表明，二维系统可能会表现出类似于二维系统中众所周知的Berezinskii-Kosterlitz-Thouless涡旋解离过渡的拓扑相变。我们在四个维度上研究了正弦-Gordon模型的适当推广及其耦合的重归一化群流方程，结果表明，频率的临界值是2 D中相应值的平方。确定临界点处异常尺寸的值（$\eta =\mathrm{1个}/32$）和超流体刚度的普遍跳跃的猜想（$4/{\pi }^2$） 提出了。