论文标题
带有轴向尺度场的费米子二元性
Fermionic dualities with axial gauge fields
论文作者
论文摘要
绘制难以解决的二元性，将相互作用的理论与非交互式相互作用的理论通常会引发对它们应用的系统的更深入的理解。但是，简化了诸如Lorentz不变性，低维度或缺乏轴向量规场之类的假设，将其应用限制为包括拓扑半学的广泛系统。在这里，我们通过开发能够计算轴向异常的轴向奴隶旋转方法来得出2+1和3+1维度的几个轴向场理论二元性。我们的2+1维二元性表明，有紧张的三维非符号拓扑绝缘子的双重临界表面理论存在。我们的3+1维二元性映射到dirac fermions to dirac fermions耦合到紧急u（1）和kalb-ramond载体和轴向仪表场。固定破坏洛伦兹不变性的轴向场构型后，此双重性图映射到相互作用的Weyl Semimetals，从而表明对非线性圆形光钙化效应的量化可以与某些相互作用具有牢固的态度。我们的工作强调了轴向和洛伦兹破裂的双重性如何改善我们对拓扑问题的理解。
The dualities that map hard-to-solve, interacting theories to free, non-interacting ones often trigger a deeper understanding of the systems to which they apply. However, simplifying assumptions such as Lorentz invariance, low dimensionality, or the absence of axial gauge fields, limit their application to a broad class of systems, including topological semimetals. Here we derive several axial field theory dualities in 2+1 and 3+1 dimensions by developing an axial slave-rotor approach capable of accounting for the axial anomaly. Our 2+1-dimensional duality suggests the existence of a dual, critical surface theory for strained three-dimensional non-symmorphic topological insulators. Our 3+1-dimensional duality maps free Dirac fermions to Dirac fermions coupled to emergent U(1) and Kalb-Ramond vector and axial gauge fields. Upon fixing an axial field configuration that breaks Lorentz invariance, this duality maps free to interacting Weyl semimetals, thereby suggesting that the quantization of the non-linear circular photogalvanic effect can be robust to certain interactions. Our work emphasizes how axial and Lorentz-breaking dualities improve our understanding of topological matter.
