Higher form symmetries of Argyres-Douglas theories
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Received: August 24, 2020 Accepted: September 12, 2020 Published: October 9, 2020
Higher form symmetries of Argyres-Douglas theories
a
Department of Mathematical Sciences, Durham University, Durham, DH1 3LE, United Kingdom b Mathematics Institute, Uppsala University, Box 480, SE-75106 Uppsala, Sweden c Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden
E-mail: [email protected], [email protected], [email protected] Abstract: 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. 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 (g, g0 ) Argyres-Douglas theories found by Cecotti-Neitzke-Vafa. In those cases where N = 1 gauge theory descriptions have been proposed for theories within this class, we find agreement between the 1-form symmetries of such N = 1 Lagrangian flows and those of the actual Argyres-Douglas fixed points, thus giving a consistency check for these proposals. Keywords: Global Symmetries, Supersymmetric Gauge Theory, Conformal Field Models in String Theory, Duality in Gauge Field Theories ArXiv ePrint: 2007.15603
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)056
JHEP10(2020)056
Michele Del Zotto,a,b,c I˜ naki Garc´ıa Etxebarriaa and Saghar S. Hosseinia
Contents 1 Introduction
1 5 5 8 11
3 Global structure of the (g, g0 ) Argyres-Douglas theories 3.1 The torsion at infinity for quasi-homogeneous threefold singularities 3.2 On N = 1 Lagrangians for N = 2 theories
11 12 13
A K-theory groups for the boundary of isolated threefold singularities
17
1
Introduction
Four-dimensional supersymmetric quantum field theories are an ideal laboratory to probe our understanding of strongly coupled relativistic systems. In this context, N = 2 supersymmetric models are particularly useful since they have enough supercharges to constrain the perturbative corrections while still allowing for interesting dynamics. In the past two decades a wide variety of new N = 2 theories have been constructed exploiting various kinds of geometric engineering techniques in string theory — for a nice review see [1]. There is no known Lagrangian description for many of the N = 2 theories so obtained, which makes it essential to develop techniques to study these theories that are independent from a Lagrangian formulation. A natural basic question in this context is to determine all the symmetries for these models, including the
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