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Anomalies of Duality Groups and Extended Conformal Manifolds

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arxiv 1803.07366 v2 pith:I3OEKE3M submitted 2018-03-20 hep-th

Nathan Seiberg , Yuji Tachikawa , Kazuya Yonekura This is my paper · ORCID
classification hep-th
keywords spacetheoryanomalyextendedmathbbanomaliesbundleduality
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

A self-duality group $\cal G$ in quantum field theory can have anomalies. In that case, the space of ordinary coupling constants $\cal M$ can be extended to include the space $\cal F$ of coefficients of counterterms in background fields. The extended space $\cal N$ forms a bundle over $\cal M$ with fiber $\cal F$, and the topology of the bundle is determined by the anomaly. For example, the ${\cal G}=SL(2,\mathbb{Z})$ duality of the 4d Maxwell theory has an anomaly, and the space ${\cal F}=S^1$ for the gravitational theta-angle is nontrivially fibered over ${\cal M}=\mathbb{H}/SL(2,\mathbb{Z})$. 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 Kahler potential on the space of exactly marginal couplings of supersymmetric theories.

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Cited by 4 Pith papers

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  1. Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies

    hep-th 2026-07 accept novelty 7.0 of 10

    An order-five Sp(4,Z) duality acts projectively on 3d U(1)^2 theories, and its hierarchy operations generate candidate bilayer quantum Hall states at 3/8+3/8 and 5/12+5/12.

  2. Higher Structures on Boundary Conformal Manifolds: Higher Berry Phase and Boundary Conformal Field Theory

    hep-th 2025-07 conditional novelty 7.0 of 10

    A 2-form higher Berry connection on boundary conformal manifolds is defined from boundary-condition-changing operator OPE phases; it reproduces the B-field and WZ term in string theory examples.

  3. Tilts from 2-Groups

    hep-th 2026-08 conditional novelty 6.0 of 10

    Line operators charged under the 1-form part of a 2-group symmetry must generically break the 0-form part, enforced by a family anomaly derived from Wess-Zumino consistency.

  4. Anomaly-induced vanishing of brane partition functions

    hep-th 2025-10 conditional novelty 6.0 of 10

    Anomalies imply vanishing brane partition functions; this yields unified derivations of the Freed-Witten and M5 shifted-quantization conditions and new S-fold D3-brane constraints.

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