Anomaly of the Electromagnetic Duality of Maxwell Theory

Chang Tse Hsieh, Yuji Tachikawa, Kazuya Yonekura

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


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.

Original languageEnglish
Article number161601
JournalPhysical review letters
Issue number16
Publication statusPublished - 2019 Oct 14

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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