Gauged 2-form Symmetries in 6D SCFTs Coupled to Gravity

TL;DR

<3-5 sentence high-level summary>This work investigates which 6D SCFT sectors can be consistently coupled to gravity and how their discrete 2-form global symmetries are affected. The authors formulate a lattice-based criterion: if the SCFT charge lattice \\Lambda_S embeds non-primitively into the gravity lattice, a torsion subgroup G = \\mathrm{tors}(\\Lambda_B/\\Lambda_S) remains unbroken by BPS strings and must be gauged. They provide both a direct lattice/geometry analysis and dual 5D perspectives (via fibre-base duality and Mordell–Weil torsion) and illustrate with explicit (2,0) and (1,0) examples, including mirror quartic, Z_5 and Z_7 quotients, and little-string theories. The results connect geometric embeddings to gauged higher-form symmetries and offer a framework for understanding the global structure of 6D supergravity coupled to SCFT sectors, with potential generalizations to Narain compactifications and related anomaly constraints.

Abstract

We study six dimensional supergravity theories with superconformal sectors (SCFTs). Instances of such theories can be engineered using type IIB strings, or more generally F-Theory, which translates field theoretic constraints to geometry. Specifically, we study the fate of the discrete 2-form global symmetries of the SCFT sectors. For both $(2,0)$ and $(1,0)$ theories we show that whenever the charge lattice of the SCFT sectors is non-primitively embedded into the charge lattice of the supergravity theory, there is a subgroup of these 2-form symmetries that remains unbroken by BPS strings. By the absence of global symmetries in quantum gravity, this subgroup much be gauged. Using the embedding of the charge lattices also allows us to determine how the gauged 2-form symmetry embeds into the 2-form global symmetries of the SCFT sectors, and we present several concrete examples, as well as some general observations. As an alternative derivation, we recover our results for a large class of models from a dual perspective upon reduction to five dimensions.

Figures (5)

• Figure 1: Depiction of M-theory duality chain leading to the same 5D $\mathcal{N}=2$ supersymmetric theories. The same theory is obtained from $T^3$ compactification of F-Theory an elliptic K3, $X$ with non-simply connected gauge group and a circle reduction of IIB on the same singular K3 with a gauged 2-form symmetry.
• Figure 2: Depiction of the mirror quartic polytope. Edge points are given in red and a slice of a 2D sub-polytope, that induces an elliptic fibration structure is highlighted. The six $A_3$ singularities between the vertices are grouped with respect to the elliptic fibration. Two $\mathfrak{e}_7$ tops are highlighted in green and blue respectively and another $\mathfrak{su}_4$ as yellow points.
• Figure 3: A fan of a 2D toric base $B$. The fan has several 1D cones, each corresponding to a curve in $\Lambda_B = H_2(B,\mathbb{Z})$. The red and blue 1D cones, ending in vertices $e_i'$ and $e_i$ all have negative self-intersection, and may be shrunk simultaneously to provide two SCFT sectors $\Gamma_1, \Gamma_2$.
• Figure 4: A fan of an extremal base $B_o$. The fan has three rays with generators $v_i$. Each of the two-dimensional cones is furthermore labelled by a lattice $\Gamma_i$ of blown-down curves and non-minimal gauge groups $\{\mathfrak{G}_i\}$ over some curves.
• Figure 5: Depiction of M-theory on $X$ with $U(1)^4 \times SU(3)/\mathbb{Z}_3$ gauge group, that exhibits two different 6D F-Theory lifts and their massless spectra. Lift $(\mathcal{A})$ exhibits an $SU(3)/\mathbb{Z}_3$ non-simply connected gauge group in 6D. The former center symmetry becomes a gauged 2-form symmetry of the $A_2^3$ SCFT sector in the second lift 6D lift $(\mathcal{B})$.