### Abstract

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 = S^{1} 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 language | English |
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Article number | 073B04 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2018 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 1 2018 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Progress of Theoretical and Experimental Physics*,

*2018*(7), [073B04]. https://doi.org/10.1093/ptep/pty069

**Anomalies of duality groups and extended conformal manifolds.** / Seiberg, Nathan; Tachikawa, Yuji; Yonekura, Kazuya.

Research output: Contribution to journal › Article

*Progress of Theoretical and Experimental Physics*, vol. 2018, no. 7, 073B04. https://doi.org/10.1093/ptep/pty069

}

TY - JOUR

T1 - Anomalies of duality groups and extended conformal manifolds

AU - Seiberg, Nathan

AU - Tachikawa, Yuji

AU - Yonekura, Kazuya

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.

UR - http://www.scopus.com/inward/record.url?scp=85055123604&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055123604&partnerID=8YFLogxK

U2 - 10.1093/ptep/pty069

DO - 10.1093/ptep/pty069

M3 - Article

VL - 2018

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 7

M1 - 073B04

ER -