Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 $$ \mathcal{N}=4 $$ gauge theory

Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide; Hilburn, Justin

doi:10.1007/jhep10(2016)108

Cited by 106 publications

(236 citation statements)

References 123 publications

(307 reference statements)

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“…in a straightforward way that we formalize in Section 3.4, generalizing a prior analysis from [78]. We carry out an explicit computation of such a deformed space, involving Wilson lines in nonabelian gauge theory, in Section 8.1 and Appendix C.1.…”

Section: Wilson Linesmentioning

confidence: 99%

Mirror symmetry and line operators

Dimofte

Garner

Geracie

et al. 2020

J. High Energ. Phys.

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We study half-BPS line operators in 3d N = 4 gauge theories, focusing in particular on the algebras of local operators at their junctions. It is known that there are two basic types of such line operators, distinguished by the SUSY subalgebras that they preserve; the two types can roughly be called "Wilson lines" and "vortex lines," and are exchanged under 3d mirror symmetry. We describe a large class of vortex lines that can be characterized by basic algebraic data, and propose a mathematical scheme to compute the algebras of local operators at their junctions -including monopole operators -in terms of this data. The computation generalizes mathematical and physical definitions/analyses of the bulk Coulombbranch chiral ring. We fully classify the junctions of half-BPS Wilson lines and of half-BPS vortex lines in abelian gauge theories with sufficient matter. We also test our computational scheme in a non-abelian quiver gauge theory, using a 3d-mirror-map of line operators from work of Assel and Gomis.

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Section: Wilson Linesmentioning

confidence: 99%

Mirror symmetry and line operators

Dimofte

Garner

Geracie

et al. 2020

J. High Energ. Phys.

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“…Promising candidates are codimension one and two 1 2 -BPS defects in 3d N = 4 theories [60,61] and codimension two and four defects in 6d (2, 0) theories, [62,63]. It would also be interesting to investigate whether certain bulk-boundary CFT data can be computed using localization methods.…”

Section: Jhep01(2017)122mentioning

confidence: 99%

Bootstrap equations for N $$ \mathcal{N} $$ = 4 SYM with defects

Liendo

Meneghelli

2017

J. High Energ. Phys.

123

174

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This paper focuses on the analysis of 4d N = 4 superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is a boundary that preserves half of the supersymmetry. After studying the constraints imposed by supersymmetry, we will obtain the Ward identities associated to two-point functions of 1 2 -BPS operators and write their solution as a superconformal block expansion. Due to a surprising connection between spacetime and R-symmetry conformal blocks, our results not only apply to 4d N = 4 superconformal theories with a boundary, but also to three more systems that have the same symmetry algebra: 4d N = 4 superconformal theories with a line defect, 3d N = 4 superconformal theories with no defect, and OSP(4 * |4) superconformal quantum mechanics. The superconformal algebra implies that all these systems possess a closed subsector of operators in which the bootstrap equations become polynomial constraints on the CFT data. We derive these truncated equations and initiate the study of their solutions.

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“…The association depends on a choice of chamber in the space of FI parameters or masses. The same data also determines certain effective mixed Chern-Simons couplings k v which enter in the central charge m · k v · ζ of the vacuum v [13]. This data is the zero-th level piece of the Symplectic Duality correspondence [14].…”

Section: Introductionmentioning

confidence: 99%