### 抄録

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.

元の言語 | 英語 |
---|---|

記事番号 | 073B04 |

ジャーナル | Progress of Theoretical and Experimental Physics |

巻 | 2018 |

発行部数 | 7 |

DOI | |

出版物ステータス | 出版済み - 7 1 2018 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### これを引用

*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.

研究成果: ジャーナルへの寄稿 › 記事

*Progress of Theoretical and Experimental Physics*, 巻. 2018, 番号 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

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 -