Higher form symmetries of Argyres-Douglas theories

Michele Del Zotto,Iñaki García Etxebarria,Saghar S. Hosseini

doi:10.1007/jhep10(2020)056

Michele Del Zotto, Iñaki García Etxebarria + Show 1 more

Open Access

https://doi.org/10.1007/jhep10(2020)056

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Abstract

We determine the structure of 1-form symmetries for all 4d mathcal{N} = 2 theories that have a geometric engineering in terms of type IIB string theory on isolated hypersurface singularities. This is a large class of models, that includes Argyres-Douglas theories and many others. Despite the lack of known gauge theory descriptions for most such theories, we find that the spectrum of 1-form symmetries can be obtained via a careful analysis of the non-commutative behaviour of RR fluxes at infinity in the IIB setup. The final result admits a very compact field theoretical reformulation in terms of the BPS quiver. We illustrate our methods in detail in the case of the ( mathfrak{g},{mathfrak{g}}^{prime } ) Argyres-Douglas theories found by Cecotti-Neitzke-Vafa. In those cases where mathcal{N} = 1 gauge theory descriptions have been proposed for theories within this class, we find agreement between the 1-form symmetries of such mathcal{N} = 1 Lagrangian flows and those of the actual Argyres-Douglas fixed points, thus giving a consistency check for these proposals.

Highlights

Argyres-Douglas theories can be realized in Type IIB superstrings on isolated hypersurface singularities [5, 6]
We determine the structure of 1-form symmetries for all 4d N = 2 theories that have a geometric engineering in terms of type IIB string theory on isolated hypersurface singularities
Despite the lack of known gauge theory descriptions for most such theories, we find that the spectrum of 1-form symmetries can be obtained via a careful analysis of the non-commutative behaviour of RR fluxes at infinity in the IIB setup

Summary

Geometric engineering and higher symmetries

In order to understand which field configurations can be put at infinity, we need to understand the Hilbert space that type IIB string theory associates to the boundary N9 := M4 × Y5. The relevant grading of Hilbert space was understood by Freed, Moore and Segal in [57, 58] They showed that whenever N9 has torsion, the operators measuring flux expectation values become non-commutative. The choices of global structure for the genuine TX6 theories are the choices of maximal isotropic L5 ⊂ Tor H3(Y5), with ∂X6 = Y5 Once we have such an L5 we have a choice for the 2-surface operators generating the 1-form symmetries of TX6: they come from the reduction of the Φσ flux operators in the IIB theory. Relatedly, introducing background fluxes for F5 at infinity will introduce background fluxes for the 1-form symmetries in the four-dimensional theory on M4

The case of hypersurface singularities

A categorical aside

The torsion at infinity for quasi-homogeneous threefold singularities

Findings

A K-theory groups for the boundary of isolated threefold singularities