TY - JOUR

T1 - Anomalies of duality groups and extended conformal manifolds

AU - Seiberg, Nathan

AU - Tachikawa, Yuji

AU - Yonekura, Kazuya

N1 - Funding Information:
The authors would like to thank C. Córdova, R. Donagi, and D. Morrison for numerous discussions on these topics and in particular about the existence of closed two-cycles in M and about the stimulating paper [13]. Useful conversations with C.-T. Hsieh, Z. Komargodski, R. Thorngren, and E. Witten are also acknowledged. The work of N.S. was supported in part by a DOE grant DE-SC0009988. The work of Y.T. was partially supported by a JSPS KAKENHI Grant-in-Aid (Wakate-A), No. 17H04837 and a JSPS KAKENHI Grant-in-Aid (Kiban-S), No. 16H06335, and also by the WPI Initiative, MEXT, Japan at IPMU, the University of Tokyo. The work of K.Y. is supported in part by the WPI Research Center Initiative (MEXT, Japan), and also supported by a JSPS KAKENHI Grant-in-Aid (Wakate-B), No. 17K14265. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies.
Publisher Copyright:
© The Author(s) 2018. Published by Oxford University Press on behalf of the Physical Society of Japan.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - 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.

AB - 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.

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U2 - 10.1093/ptep/pty069

DO - 10.1093/ptep/pty069

M3 - Article

AN - SCOPUS:85055123604

VL - 2018

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 7

M1 - 073B04

ER -