论文标题
仪表大电量
Gauge Invariance at Large Charge
论文作者
论文摘要
具有全局对称性的量子场理论在大电荷极限下大大简化了，从而可以通过在保守电荷的逆权力中通过半经典扩展来计算相关器。衡量对称方法的概括面临定义独立于量规的可观察结果的问题，因此尚未开发出来。我们采用大电荷扩展来计算关键的Abelian Higgs模型中携带$ U（1）$ U（1）$ u（1）$ u（1）$ d = 4-ε$维度的缩放维度，以指导和临时收费和$ε$扩展中的所有订单。值得注意的是，结果与我们对运算符$ ϕ^q（x）$在Landau仪表中的三环缩放维度的独立图表计算相匹配。我们认为，这种匹配是dirac类型的仪表独立的两点函数与landau仪表中$ ϕ^q（x）$的量规依赖的两点函数之间的等效性的结果。因此，我们对定义量规非依赖指数的问题有了新的启示，这些指数在关键超导体的文献中一直存在争议，并为规范理论中的大型方法奠定了基础。
Quantum field theories with global symmetries simplify considerably in the large-charge limit allowing to compute correlators via a semiclassical expansion in the inverse powers of the conserved charges. A generalization of the approach to gauge symmetries has faced the problem of defining gauge-independent observables and, therefore, has not been developed so far. We employ the large-charge expansion to calculate the scaling dimension of the lowest-lying operators carrying $U(1)$ charge $Q$ in the critical Abelian Higgs model in $D=4-ε$ dimensions to leading and next-to-leading orders in the charge and all orders in the $ε$ expansion. Remarkably, the results match our independent diagrammatic computation of the three-loop scaling dimension of the operator $ϕ^Q(x)$ in the Landau gauge. We argue that this matching is a consequence of the equivalence between the gauge-independent dressed two-point function of Dirac type with the gauge-dependent two-point function of $ϕ^Q(x)$ in the Landau gauge. We, therefore, shed new light on the problem of defining gauge-independent exponents which has been controversial in the literature on critical superconductors as well as lay the foundation for large-charge methods in gauge theories.
