Supersymmetric vortex defects in two dimensions

Hosomichi, Kazuo; Lee, Sungjay; Okuda, Takuya

doi:10.1007/jhep01(2018)033

Cited by 20 publications

(21 citation statements)

References 44 publications

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“…They may also be understood as dimensional reductions of supersymmetric surface operators in 4d gauge theories: the basic Gukov-Witten surface operators [11,25,26] and their 4d N = 2 analogues [15,[27][28][29][30], studied and generalized in many later works -a small sampling includes [31][32][33][34][35][36][37][38][39] (see [40] for a clear review). Compactifying further to two dimensions, vortex lines becomes twist fields, which played a fundamental role in T-duality/mirror symmetry [41] and were recently reexamined by [42,43].…”

Section: Contentsmentioning

confidence: 99%

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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: Contentsmentioning

confidence: 99%

“…It turns out that the space of viable linear combinations is reduced to either V ± 1 or ∓V ± 2 when matching the other relations. 43 We choose…”

Section: C4 Matching Across Mirror Symmetrymentioning

confidence: 99%

Mirror symmetry and line operators

Dimofte

Garner

Geracie

et al. 2020

J. High Energ. Phys.

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“…Instead of solving the Eqs. (65) and studying the Dirac operator on the space of solutions, we modify the Dirac operator on the ambient space M, by coupling it to the exterior powers Λ i E of the vector bundle E where the Eqs. (65) take values:…”

Section: Twisted Witten Index and Generalized Hitchin Equationsmentioning

confidence: 99%

BPS/CFT correspondence IV: sigma models and defects in gauge theory

Nekrasov

2018

Lett Math Phys

127

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Quantum field theory L 1 on spacetime X 1 can be coupled to another quantum field theory L 2 on a spacetime X 2 via the third quantum field theory L 12 living on X 12 = X 1 ∩X 2 . We explore several such constructions with two and four dimensional X 1 , X 2 's and zero and two dimensional X 12 's, in the context of N = 2 supersymmetry, non-perturbative Dyson-Schwinger equations, and BPS/CFT correspondence. The companion paper [99] will show that the BPZ and KZ equations of two dimensional conformal field theory are obeyed by the half-BPS surface defects in quiver N = 2 gauge theories.

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“…Finally, one can compute correlators by adding insertions of BPS operators coming either from the N = (2, 2) multiplets (e.g. [47,48]) or from the bulk theory. The latter have been extensively discussed in section 6, whether the former appear in the quantum mechanics as insertions of local operators at the intersection point, namely t = 0.…”

Section: Jhep09(2020)185mentioning

confidence: 99%

Topological correlators and surface defects from equivariant cohomology

Panerai

Pittelli

Polydorou

2020

J. High Energ. Phys.

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We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

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Supersymmetric vortex defects in two dimensions

Cited by 20 publications

References 44 publications

Mirror symmetry and line operators

Mirror symmetry and line operators

BPS/CFT correspondence IV: sigma models and defects in gauge theory

Topological correlators and surface defects from equivariant cohomology

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