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.
Highlights
Theories in geometric terms using F-Theory on non-compact singular Calabi-Yau varieties
We study the fate of the discrete 2-form global symmetries of the superconformal sectors (SCFTs) 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
For such ‘extremal’ cases, we find a simple condition that determines if part of the group of global 2-form symmetries becomes gauged when coupling the SCFT sector to gravity
Summary
We are going to take the following perspective. Assume that we have found an embedding. If we reintroduce gravity, this introduces new BPS strings associated with the elements of Λ5,21 These will in general transform under GS and break it to a subgroup G. The presence of this torsional group means that ΛS is embedded in a non-minimal way in Λ5,21, i.e. ΛS = (ΛS ⊗ Q) ∩ Λ5,21 This implies that the inner product of elements of Λ5,21 with elements of ΛS, which results in charges of BPS strings under the 2-form symmetries of the conformal sectors to be non-minimal as well. As is evident from (3.7), elements of G form a subset of elements of GS = Λ∗S/ΛS This in particular allows to determine which subgroup of GS becomes gauged upon coupling the chosen collection of SCFTs to gravity. Note that for a specific choice of ΛS, G is not unique but depends on the embedding ΛS → Λ5,21
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