论文标题
在有限温度下，在量规理论和戈德斯通定理中的狄拉克模式的定位
Localisation of Dirac modes in gauge theories and Goldstone's theorem at finite temperature
论文作者
论文摘要
我讨论了用$ n_f $堕落的费米子的手性限制局部接近零迪拉克模式的有限密度的可能影响。我特别关注的是，戈德斯通定理的有限温度版本预测的无质量准粒子激发的命运，为此，我为此提供了基于欧几里得$ {\ rm su}（\ rm su}（n_f）_a $ ward-ward-ward-ward-takahashi Identity的替代性和广义证明。我表明，局部接近零模式可以导致伪级伪尺度相关器，该相关器可在手性极限中修改这种身份。结果，尽管非零的手性冷凝物，尽管理论的谱系可能会从理论的光谱中消失。可能会有三种不同的情况，具体取决于迁移率边缘和费米质量比率的详细行为，我被证明是重态化组不变的数量。
I discuss the possible effects of a finite density of localised near-zero Dirac modes in the chiral limit of gauge theories with $N_f$ degenerate fermions. I focus in particular on the fate of the massless quasi-particle excitations predicted by the finite-temperature version of Goldstone's theorem, for which I provide an alternative and generalised proof based on a Euclidean ${\rm SU}(N_f)_A$ Ward-Takahashi identity. I show that localised near-zero modes can lead to a divergent pseudoscalar-pseudoscalar correlator that modifies this identity in the chiral limit. As a consequence, massless quasi-particle excitations can disappear from the spectrum of the theory in spite of a non-zero chiral condensate. Three different scenarios are possible, depending on the detailed behaviour in the chiral limit of the ratio of the mobility edge and the fermion mass, which I prove to be a renormalisation-group invariant quantity.
