On the anomaly of the electromagnetic duality of the Maxwell theory

Chang Tse Hsieh, Yuji Tachikawa, Kazuya Yonekura

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Abstract

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, and 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 SPT 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.

Original language English Unknown Journal Published - 2019 May 22

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