Supersymmetric Boundary Conditions in 3D N=2 Theories

Okazaki, Tadashi; Yamaguchi, Satoshi

doi:10.1090/pspum/088/01459

Cited by 20 publications

(52 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Second, we claim (conjecturally) that in the fully reduced theory T 2d , we can deform the twist Q 0,0 to any Q ζ,0 or Q 0,ζ without changing the category of half-BPS boundary 45 The quantization parameter kt appearing on the r.h.s. of (7.65) enters as a parameter of the canonical coisotropic brane Bcc in the definition of I D. The precise value is unimportant, since we know (section 7.3.2) that categories O k t ,m R H for different kt are derived equivalent.…”

Section: Relation To Derived Categories Omentioning

confidence: 94%

“…Such half-BPS boundary conditions for 3d N = 2 theories were studied in [45,46], and play a central role in the 4d-2d correspondence [47], where they are labelled by four-manifolds with boundary.…”

Section: Jhep10(2016)108mentioning

confidence: 99%

“…a cocharacter A ∈ Hom(U(1), G). The quantumcorrected chiral-ring relations take the form [5,107,108] 45) where m C are complex mass deformation parameters and P A,B (ϕ, m C ) is a product of contributions from all hypermultiplets…”

Section: Coulomb-branch Imagementioning

confidence: 99%

“…45 Similarly, in the A-twisted sigma-model to the Coulomb branch, the FI parameter t R induces a superpotential with real part h t = t R · µ C,R , such that the image of I D becomes precisely…”

Section: Relation To Derived Categories Omentioning

confidence: 99%

See 3 more Smart Citations

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

Bullimore

Dimofte

Gaiotto

et al. 2016

J. High Energ. Phys.

107

229

View full text Add to dashboard Cite

Abstract:We introduce several families of N = (2, 2) UV boundary conditions in 3d N = 4 gauge theories and study their IR images in sigma-models to the Higgs and Coulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs-and Coulomb-branch operators, respectively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studying two-dimensional compactifications of 3d N = 4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality -an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.

show abstract

Section: Relation To Derived Categories Omentioning

confidence: 94%

Section: Jhep10(2016)108mentioning

confidence: 99%

Section: Coulomb-branch Imagementioning

confidence: 99%

Section: Relation To Derived Categories Omentioning

confidence: 99%

See 2 more Smart Citations

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

Bullimore

Dimofte

Gaiotto

et al. 2016

J. High Energ. Phys.

107

229

View full text Add to dashboard Cite

show abstract

“…theories in flat space, [15]. Unlike the case of flat space where one projects constant spinors, in curved spaces one has to project spinors that are in general non-trivial functions of the spacetime coordinates.…”

Section: Jhep07(2016)126mentioning

confidence: 99%

N $$ \mathcal{N} $$ =2 supersymmetric field theories on 3-manifolds with A-type boundaries

Aprile

Niarchos

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

General half-BPS A-type boundary conditions are formulated for N = 2 supersymmetric field theories on compact 3-manifolds with boundary. We observe that under suitable conditions manifolds of the real A-type admitting two complex supersymmetries (related by charge conjugation) possess, besides a contact structure, a natural integrable toric foliation. A boundary, or a general co-dimension-1 defect, can be inserted along any leaf of this preferred foliation to produce manifolds with boundary that have the topology of a solid torus. We show that supersymmetric field theories on such manifolds can be endowed with half-BPS A-type boundary conditions. We specify the natural curved space generalization of the A-type projection of bulk supersymmetries and analyze the resulting A-type boundary conditions in generic 3d non-linear sigma models and YM/CS-matter theories.

show abstract

Fivebranes and 4-Manifolds

Gadde

Gukov

Putrov

2016

Progress in Mathematics

179

390

View full text Add to dashboard Cite

Abstract:We describe rules for building 2d theories labeled by 4-manifolds. Using the proposed dictionary between building blocks of 4-manifolds and 2d N = (0, 2) theories, we obtain a number of results, which include new 3d N = 2 theories T [M 3 ] associated with rational homology spheres and new results for Vafa-Witten partition functions on 4-manifolds. In particular, we point out that the gluing measure for the latter is precisely the superconformal index of 2d (0, 2) vector multiplet and relate the basic building blocks with coset branching functions. We also offer a new look at the fusion of defect lines / walls, and a physical interpretation of the 4d and 3d Kirby calculus as dualities of 2d N = (0, 2) theories and 3d N = 2 theories, respectively.

show abstract

Supersymmetric Boundary Conditions in 3D N=2 Theories

Cited by 20 publications

References 28 publications

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

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

N $$ \mathcal{N} $$ =2 supersymmetric field theories on 3-manifolds with A-type boundaries

Fivebranes and 4-Manifolds

Contact Info

Product

Resources

About