Anomalies of duality groups and extended conformal manifolds

Nathan Seiberg, Yuji Tachikawa, Kazuya Yonekura

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)


A self-duality group G in quantum field theory can have anomalies. In that case, the space of ordinary coupling constants M can be extended to include the space F of coefficients of counterterms in background fields. The extended space N forms a bundle over M with fiber F, and the topology of the bundle is determined by the anomaly. For example, the G = SL(2, Z) duality of the 4D Maxwell theory has an anomaly, and the space F = S1 for the gravitational theta angle is nontrivially fibered over M = H/SL(2, Z). We will explain a simple method to determine the anomaly when the 4D theory is obtained by compactifying a 6D theory on a Riemann surface in terms of the anomaly polynomial of the parent 6D theory. Our observations resolve an apparent contradiction associated with the global structure of the Kähler potential on the space of exactly marginal couplings of supersymmetric theories.

Original languageEnglish
Article number073B04
JournalProgress of Theoretical and Experimental Physics
Issue number7
Publication statusPublished - Jul 1 2018

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)


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