Blocks and vortices in the 3d ADHM quiver gauge theory

Samuel, Crew,; Dorey, Nick; Zhang, Daniel

doi:10.1007/jhep03(2021)234

Cited by 11 publications

(7 citation statements)

References 68 publications

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“…This ensures that there are no additional non-compact 2d degrees of freedom at the boundary. This is discussed in section 4.4 of [18] and explored in [34] for a theory with adjoint matter. In this work we focus on supersymmetric QED, leaving general abelian theories to appendix B.…”

Section: Abelian Theoriesmentioning

confidence: 99%

Boundaries, Vermas and factorisation

Bullimore

Samuel

Zhang

2021

J. High Energ. Phys.

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We revisit the factorisation of supersymmetric partition functions of 3d $$ \mathcal{N} $$ N = 4 gauge theories. The building blocks are hemisphere partition functions of a class of UV $$ \mathcal{N} $$ N = (2, 2) boundary conditions that mimic the presence of isolated vacua at infinity in the presence of real mass and FI parameters. These building blocks can be unambiguously defined and computed using supersymmetric localisation. We show that certain limits of these hemisphere partition functions coincide with characters of lowest weight Verma mod- ules over the quantised Higgs and Coulomb branch chiral rings. This leads to expressions for the superconformal index, twisted index and S3 partition function in terms of such characters. On the way we uncover new connections between boundary ’t Hooft anomalies, hemisphere partition functions and lowest weights of Verma modules.

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Section: Abelian Theoriesmentioning

confidence: 99%

Boundaries, Vermas and factorisation

Bullimore

Samuel

Zhang

2021

J. High Energ. Phys.

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“…This can lead to a convenient method to compute boundary amplitudes using supersymmetric localisation. Such boundary conditions preserving N = (2, 2) supersymmetry were first considered in [15], and have been studied further in [20,66].…”

Section: The Ideamentioning

confidence: 99%

3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve

Bullimore

Zhang

2022

SciPost Phys.

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This paper studies 3d3d\mathcal{N}=4𝒩=4 supersymmetric gauge theories on an elliptic curve, with the aim to provide a physical realisation of recent constructions in equivariant elliptic cohomology of symplectic resolutions. We first study the Berry connection for supersymmetric ground states in the presence of mass parameters and flat connections for flavour symmetries, which results in a natural construction of the equivariant elliptic cohomology variety of the Higgs branch. We then investigate supersymmetric boundary conditions and show from an analysis of boundary ’t Hooft anomalies that their boundary amplitudes represent equivariant elliptic cohomology classes. We analyse two distinguished classes of boundary conditions known as exceptional Dirichlet and enriched Neumann, which are exchanged under mirror symmetry. We show that the boundary amplitudes of the latter reproduce elliptic stable envelopes introduced by Aganagic-Okounkov, and relate boundary amplitudes of the mirror symmetry interface to the mother function in equivariant elliptic cohomology. Finally, we consider correlation functions of Janus interfaces for varying mass parameters, recovering the chamber R-matrices of elliptic integrable systems.

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“…With the systematic study of rigid supersymmetry on curved manifolds [15,16], all possible manifolds on which at least N = 2 supersymmetry can be preserved have been classified and corresponding partition functions Z M 3 have been computed, with the possible exception of the 3-torus T 3 [17][18][19][20]. Among them is the partition function on a manifold given by the twisted product of a disk (2d hemisphere) and a circle: D 2 × q S 1 [21][22][23], where q is a deformation parameter of D 2 . This partition function is also known as a holomorphic block.…”

Section: Introductionmentioning

confidence: 99%

Stokes phenomena in 3d $$ \mathcal{N} $$ = 2 SQED2 and $$ \mathbbm{CP} $$1 models

Jain

Manna

2021

J. High Energ. Phys.

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We propose a novel approach of uncovering Stokes phenomenon exhibited by the holomorphic blocks of $$ \mathbbm{CP} $$ CP 1 model by considering it as a specific decoupling limit of SQED2 model. This approach involves using a ℤ3 symmetry that leaves the supersymmetric parameter space of SQED2 model invariant to transform a pair of SQED2 holomorphic blocks to get two new pairs of blocks. The original pair obtained by solving the line operator identities of the SQED2 model and the two new transformed pairs turn out to be related by Stokes-like matrices. These three pairs of holomorphic blocks can be reduced to the known triplet of $$ \mathbbm{CP} $$ CP 1 blocks in a particular decoupling limit where two of the chiral multiplets in the SQED2 model are made infinitely massive. This reduction then correctly reproduces the Stokes regions and matrices of the $$ \mathbbm{CP} $$ CP 1 blocks. Along the way, we find six pairs of SQED2 holomorphic blocks in total, which lead to six Stokes-like regions covering uniquely the full parameter space of the SQED2 model.

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Blocks and vortices in the 3d ADHM quiver gauge theory

Cited by 11 publications

References 68 publications

Boundaries, Vermas and factorisation

Boundaries, Vermas and factorisation

3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve

Stokes phenomena in 3d $$ \mathcal{N} $$ = 2 SQED2 and $$ \mathbbm{CP} $$1 models

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