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.
Highlights
Six-dimensional supeconformal field theories (SCFTs) provide a higher-dimensional perspective on many aspects of lower-dimensional quantum field theories
These different possibilities are conveniently handled using the F-theory characterization of 6D SCFTs, where these moduli correspond to resolution parameters of curves
The rest of this paper is organized as follows: first, in section 2 we discuss in general terms the automorphism group for a lattice of strings, and the physical data it captures in compactifications of a 6D SCFT, and compute it for all 6D SCFTs
Summary
Six-dimensional supeconformal field theories (SCFTs) provide a higher-dimensional perspective on many aspects of lower-dimensional quantum field theories. Though there is still a notion of a fundamental domain of moduli space for a theory with T tensor multiplets, the orbits of this patch under the automorphism group sometimes do not produce a tessellation of RT , leading to non-trivial forbidden zones These different possibilities are conveniently handled using the F-theory characterization of 6D SCFTs, where these moduli correspond to resolution parameters of curves. The rest of this paper is organized as follows: first, in section 2 we discuss in general terms the automorphism group for a lattice of strings, and the physical data it captures in compactifications of a 6D SCFT, and compute it for all 6D SCFTs. Section 3 studies the structure of the tensor branch moduli space, as dictated by the automorphism group. Some additional details on how to calculate the anomaly polynomial of a 6D SCFT via “analytic continuation” in the rank of the gauge groups present on the tensor branch are presented in appendix A
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