2018/03/23 by Seung-Joo Lee, Diego Regalado, Timo Weigand
Mathematics · Physics and Astronomy · #Abelian group #Black Holes and Theoretical Physics #Gauge theory #Geometry #Homogeneous space #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Supergravity #Supersymmetry #Theoretical physics #hep-th
paper · pdf · doi:10.1007/jhep11(2018)147
41 pages; v2: references added, typos corrected, footnotes 8 and 13 added
arxiv created 2018/03/23 · openalex publication_date 2018/11/01 · arxiv updated 2018/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract We study the behaviour of abelian gauge symmetries in six-dimensional N = (1 , 0) theories upon decoupling gravity and investigate abelian flavour symmetries in the context of 6d N = (1 , 0) SCFTs. From a supergravity perspective, the anomaly cancellation mechanism implies that abelian gauge symmetries can only survive as global symmetries as gravity is decoupled. The flavour symmetries obtained in this way are shown to be free of ABJ anomalies, and their ’t Hooft anomaly polynomial in the decoupling limit is obtained explicitly. In an F-theory realisation the decoupling of abelian gauge symmetries implies that a mathematical object known as the height pairing of a rational section is not contractible as a curve on the base of an elliptic Calabi-Yau threefold. We prove this prediction from supergravity by making use of the properties of the Mordell-Weil group of rational sections. In the second part of this paper we study the appearance of abelian flavour symmetries in 6d N = (1 , 0) SCFTs. We elucidate both the geometric origin of such flavour symmetries in F-theory and their field theoretic interpretation in terms of suitable linear combinations of geometrically massive U(1)s. Our general results are illustrated in various explicit examples.