Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba 277-8583, Japan.
Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan.
Phys Rev Lett. 2019 Oct 18;123(16):161601. doi: 10.1103/PhysRevLett.123.161601.
We consider the (3+1)-dimensional Maxwell theory in the situation where going around nontrivial paths in the spacetime involves the action of the duality transformation exchanging the electric field and the magnetic field, as well as its SL(2,Z) generalizations. We find that the anomaly of this system in a particular formulation is 56 times that of a Weyl fermion. This result is derived in two independent ways: one is by using the bulk symmetry protected topological phase in (4+1) dimensions characterizing the anomaly, and the other is by considering the properties of a (5+1)-dimensional superconformal field theory known as the E-string theory. This anomaly of the Maxwell theory plays an important role in the consistency of string theory.
我们研究了（3+1）维麦克斯韦理论在时空中小绕非平凡路径的情况，其中包括对偶变换的作用，该变换交换了电场和磁场及其 SL(2,Z)推广。我们发现，在特定形式下，该系统的反常是 Weyl 费米子的 56 倍。这一结果是通过两种独立的方法得出的：一种是利用（4+1）维中保护拓扑相的体对称性来描述反常，另一种是考虑一种称为 E-弦理论的（5+1）维超共形场论的性质。麦克斯韦理论的这种反常在弦论的一致性中起着重要作用。
