TY - JOUR

T1 - On the anomaly of the electromagnetic duality of the Maxwell theory

AU - Hsieh, Chang Tse

AU - Tachikawa, Yuji

AU - Yonekura, Kazuya

N1 - Publisher Copyright:
Copyright © 2019, The Authors. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2019/5/22

Y1 - 2019/5/22

N2 - 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.

AB - 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.

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