Non-Perturbative Schwinger-Dyson Equations for 3d ${\cal N} = 4$ Gauge Theories

Haouzi, Nathan

doi:10.48550/arxiv.2009.08989

Cited by 3 publications

(2 citation statements)

References 103 publications

(210 reference statements)

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“…Forgetting the prefactor, this expression coincides with the limit of the fundamental vortex qqcharacter of the 3D N = 4 U(2) gauge theory with two flavors [54], it is a polynomial of degree N = 2 when κ = 0. This qq-character corresponds to the vortex partition function in the presence of a codimension two defect (wrapping S 1 ) supporting a N = (2, 2) quantum mechanics.…”

Section: Algebraic Engineeringmentioning

confidence: 71%

Engineering 3D $\mathcal{N}=2$ theories using the quantum affine $\mathfrak{sl}(2)$ algebra

Bourgine¹

2021

Preprint

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The algebraic engineering technique is applied to a class of 3D N = 2 gauge theories on the omega-deformed background R 2 ε × S 1 . The vortex partition function and the fundamental qqcharacter are obtained from a network of intertwiners between representations of the shifted (or asymptotic) quantum affine sl(2) algebra. This network involves two types of representations, the prefundamental representation of Hernandez-Jimbo, and a new vertex representation acting on a bosonic Fock space. The brane system associated to this network is identified: D3 branes carry the prefundamental module while NS5-branes (+D5) support the Fock module. In the process, we highlight the role of shifted quantum algebras in implementing the Higgsing procedure.

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Section: Algebraic Engineeringmentioning

confidence: 71%

Engineering 3D $\mathcal{N}=2$ theories using the quantum affine $\mathfrak{sl}(2)$ algebra

Bourgine¹

2021

Preprint

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“…As before, one expects the regular 3d-1d contribution to be annihilated by a quantum operator. The systematic gauge theoretic study of such operator identities involve qq-characters or Schwinger-Dyson equations [56,57], whose algebraic meaning is recalled in section 4. At present, we do not have a clear interpretation from the integrable system viewpoint, however, following [58][59][60], one may suspect some relation between our system and qKZ equations [61], perhaps through spectral duality [62][63][64].…”

Section: Semiclassical Analysismentioning

confidence: 99%

Intersecting defects and supergroup gauge theory

Kimura

Nieri²

2021

J. Phys. A: Math. Theor.

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We consider 5d supersymmetric gauge theories with unitary groups in the Ωbackground and study codim-2/4 BPS defects supported on orthogonal planes intersecting at the origin along a circle. The intersecting defects arise upon implementing the most generic Higgsing (geometric transition) to the parent higher dimensional theory, and they are described by pairs of 3d supersymmetric gauge theories with unitary groups interacting through 1d matter at the intersection. We explore the relations between instanton and generalized vortex calculus, pointing out a duality between intersecting defects subject to the Ω-background and a deformation of supergroup gauge theories, the exact supergroup point being achieved in the self-dual or unrefined limit. Embedding our setup into refined topological strings and in the simplest case when the parent 5d theory is Abelian, we are able to identify the supergroup theory dual to the intersecting defects as the supergroup version of refined Chern-Simons theory via open/closed duality. We also discuss the BPS/CFT side of the correspondence, finding an interesting large rank duality with super-instanton counting.

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Intersecting Defects and Supergroup Gauge Theory

Kimura,

Nieri

2021

Preprint

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We consider 5d supersymmetric gauge theories with unitary groups in the Ωbackground and study codim-2/4 BPS defects supported on orthogonal planes intersecting at the origin along a circle. The intersecting defects arise upon implementing the most generic Higgsing (geometric transition) to the parent higher dimensional theory, and they are described by pairs of 3d supersymmetric gauge theories with unitary groups interacting through 1d matter at the intersection. We explore the relations between instanton and generalized vortex calculus, pointing out a duality between intersecting defects subject to the Ω-background and a deformation of supergroup gauge theories, the exact supergroup point being achieved in the self-dual or unrefined limit. Embedding our setup into refined topological strings and in the simplest case when the parent 5d theory is Abelian, we are able to identify the supergroup theory dual to the intersecting defects as the supergroup version of refined Chern-Simons theory via open/closed duality. We also discuss the BPS/CFT side of the correspondence, finding an interesting large rank duality with super-instanton counting.

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Non-Perturbative Schwinger-Dyson Equations for 3d ${\cal N} = 4$ Gauge Theories

Cited by 3 publications

References 103 publications

Engineering 3D $\mathcal{N}=2$ theories using the quantum affine $\mathfrak{sl}(2)$ algebra

Engineering 3D $\mathcal{N}=2$ theories using the quantum affine $\mathfrak{sl}(2)$ algebra

Intersecting defects and supergroup gauge theory

Intersecting Defects and Supergroup Gauge Theory

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