Unifying the 6D $\mathcal{N}=(1,1)$ String Landscape

TL;DR

This paper introduces a unifying framework for classifying six-dimensional string theory moduli spaces with  supersymmetry, connecting orbifold constructions with 2D conformal field theories and revealing numerous new moduli spaces.

Contribution

It proposes a rank reduction map organizing all known  6D string moduli spaces, including new classes, and completes the classification of nonabelian gauge symmetries in 7D.

Findings

Identifies 47 total moduli spaces, with 30 previously unknown.

Connects cyclic orbifolds to meromorphic 2D (s)CFTs with specific central charges.

Provides a full classification of nonabelian gauge symmetries in 7D.

Abstract

We propose an organizing principle for string theory moduli spaces in six dimensions with $\mathcal{N} = (1,1)$, based on a rank reduction map, into which all known constructions fit. In the case of cyclic orbifolds, which are the main focus of the paper, we make an explicit connection with meromorphic 2D (s)CFTs with $c = 24$ ($c = 12$) and show how these encode every possible gauge symmetry enhancement in their associated 6D theories. These results generalize naturally to non-cyclic orbifolds, into which the only known string construction (to our awareness) also fits. This framework suggests the existence of a total of 47 moduli spaces: the Narain moduli space, 23 of cyclic orbifold type and 23 of non-cyclic type. Of these only 17 have known string constructions. Among the 30 new moduli spaces, 15 correspond to pure supergravity, for a total of 16 such spaces. A full classification of nonabelian gauge symmetries is given, and as a byproduct we complete the one for seven dimensions, in which only those of theories with heterotic descriptions were known exhaustively.