The hitchhiker's guide to 4d $\mathcal{N}=2$ superconformal field theories

Akhond, Mohammad; Tamargo, Guillermo Arias; Mininno, Alessandro; Sun, Haoyu; Sun, Zhengdi; Wang, Yifan; Xu, Fengjun

doi:10.21468/scipostphyslectnotes.64

Cited by 6 publications

(1 citation statement)

References 318 publications

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“…Striking examples of trapped 1-form symmetries are provided by Argyres-Douglas (AD) theories of type AD[G, G ] that are constructed by compactifying 6d N = (2, 0) theories on a sphere with a single puncture that is irregular. Such AD theories, and also a vast number of other 4d N = 2 SCFTs, can also be constructed by compactifying Type IIB on canonical isolated hypersurface Calabi-Yau three-fold singularities (IHS) X [17,29,30,36,55,[75][76][77][78][79][80][81][82][83][84][85][86], for a recent review see [87]. Using string theoretic methods, the 1-form symmetries of these 4d N = 2 SCFTs can be computed from the topology of the boundary 5-manifold ∂ X [17,29,30,36,55].…”

Section: Introductionmentioning

confidence: 99%

Relative defects in relative theories: Trapped higher-form symmetries and irregular punctures in class S

et al. 2022

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A relative theory is a boundary condition of a higher-dimensional topological quantum field theory (TQFT), and carries a non-trivial defect group formed by mutually non-local defects living in the relative theory. Prime examples are 6d6d\mathcal{N}=(2,0)𝒩=(2,0) theories that are boundary conditions of 7d7d TQFTs, with the defect group arising from surface defects. In this paper, we study codimension-two defects in 6d6d\mathcal{N}=(2,0)𝒩=(2,0) theories, and find that the line defects living inside these codimension-two defects are mutually non-local and hence also form a defect group. Thus, codimension-two defects in a 6d6d\mathcal{N}=(2,0)𝒩=(2,0) theory are relative defects living inside a relative theory. These relative defects provide boundary conditions for topological defects of the 7d7d bulk TQFT. A codimension-two defect carrying a non-trivial defect group acts as an irregular puncture when used in the construction of 4d4d\mathcal{N}=2𝒩=2 Class S theories. The defect group associated to such an irregular puncture provides extra “trapped” contributions to the 1-form symmetries of the resulting Class S theories. We determine the defect groups associated to large classes of both conformal and non-conformal irregular punctures. Along the way, we discover many new classes of irregular punctures. A key role in the analysis of defect groups is played by two different geometric descriptions of the punctures in Type IIB string theory: one provided by isolated hypersurface singularities in Calabi-Yau threefolds, and the other provided by ALE fibrations with monodromies.

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Section: Introductionmentioning

confidence: 99%

Relative defects in relative theories: Trapped higher-form symmetries and irregular punctures in class S

et al. 2022

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A tale of 2-groups: Dp(USp(2N)) theories

Carta

Giacomelli

Mekareeya

et al. 2023

J. High Energ. Phys.

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A 1-form symmetry and a 0-form symmetry may combine to form an extension known as the 2-group symmetry. We find the presence of the latter in a class of Argyres-Douglas theories, called Dp(USp(2N)), which can be realized by ℤ2-twisted compactification of the 6d $$ \mathcal{N} $$ N = (2, 0) of the D-type on a sphere with an irregular twisted puncture and a regular twisted full puncture. We propose the 3d mirror theories of general Dp(USp(2N)) theories that serve as an important tool to study their flavor symmetry and Higgs branch. Yet another important result is presented: we elucidate a technique, dubbed “bootstrap”, which generates an infinite family of $$ {D}_p^b(G) $$ D p b G theories, where for a given arbitrary group G and a parameter b, each theory in the same family has the same number of mass parameters, same number of marginal deformations, same 1-form symmetry, and same 2-group structure. This technique is utilized to establish the presence or absence of the 2-group symmetries in several classes of $$ {D}_p^b(G) $$ D p b G theories. In this regard, we find that the Dp(USp(2N)) theories constitute a special class of Argyres-Douglas theories that have a 2-group symmetry.

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Disconnected gauge groups in the infrared

Arias-Tamargo,

De Marco

2024

J. High Energ. Phys.

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Gauging a discrete 0-form symmetry of a QFT is a procedure that changes the global form of the gauge group but not its perturbative dynamics. In this work, we study the Seiberg-Witten solution of theories resulting from the gauging of charge conjugation in 4d $$ \mathcal{N} $$ N = 2 theories with SU(N) gauge group and fundamental hypermultiplets. The basic idea of our procedure is to identify the ℤ2 action at the level of the SW curve and perform the quotient, and it should also be applicable to non-lagrangian theories. We study dynamical aspects of these theories such as their moduli space singularities and the corresponding physics; in particular, we explore the complex structure singularity arising from the quotient procedure. We also discuss some implications of our work in regards to three problems: the geometric classification of 4d SCFTs, the study of non-invertible symmetries from the SW geometry, and the String Theory engineering of theories with disconnected gauge groups.

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The hitchhiker's guide to 4d $\mathcal{N}=2$ superconformal field theories

Cited by 6 publications

References 318 publications

Relative defects in relative theories: Trapped higher-form symmetries and irregular punctures in class S

Relative defects in relative theories: Trapped higher-form symmetries and irregular punctures in class S

A tale of 2-groups: Dp(USp(2N)) theories

Disconnected gauge groups in the infrared

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