Green-Schwarz Automorphisms and 6D SCFTs

TL;DR

This paper computes the automorphism group of the string charge lattice in 6D SCFTs, revealing how discrete symmetries influence the moduli space and dualities upon compactification, with implications for string constructions.

Contribution

It provides the first systematic computation of automorphisms of the string charge lattice in 6D SCFTs, linking lattice symmetries to geometric and duality properties.

Findings

Automorphism group of the lattice is explicitly computed.

Discrete symmetries determine the structure of the moduli space.

Automorphisms generate Seiberg-like dualities and quotient theories.

Abstract

All known interacting 6D superconformal field theories (SCFTs) have a tensor branch which includes anti-chiral two-forms and a corresponding lattice of string charges. Automorphisms of this lattice preserve the Dirac pairing and specify discrete global and gauge symmetries of the 6D theory. In this paper we compute this automorphism group for 6D SCFTs. This discrete data determines the geometric structure of the moduli space of vacua. Upon compactification, these automorphisms generate Seiberg-like dualities, as well as additional theories in discrete quotients by the 6D global symmetries. When a perturbative realization is available, these discrete quotients correspond to including additional orientifold planes in the string construction.