6d SCFTs and U(1) Flavour Symmetries

TL;DR

This paper investigates abelian gauge and flavor symmetries in 6d N=(1,0) theories, showing how they behave upon decoupling gravity, their anomaly properties, and their geometric origins in F-theory.

Contribution

It provides a detailed analysis of abelian symmetries in 6d SCFTs, linking supergravity, anomaly cancellation, and F-theory geometry, with explicit examples.

Findings

Abelian gauge symmetries become global flavor symmetries when gravity is decoupled.

The 't Hooft anomaly polynomial for these flavor symmetries is explicitly derived.

The height pairing of rational sections is shown to be non-contractible in F-theory geometry.

Abstract

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.