Related papers: Abelian dualities of $\mathcal{N}=(0,4)$ boundary …
We evaluate half-indices of $\mathcal{N}=(2,2)$ half-BPS boundary conditions in 3d $\mathcal{N}=4$ supersymmetric Abelian gauge theories. We confirm that the Neumann boundary condition is dual to the generic Dirichlet boundary condition for…
We propose confining dualities of $\mathcal{N}=(0,2)$ half-BPS boundary conditions in 3d $\mathcal{N}=2$ supersymmetric $SU(N)$, $USp(2n)$ and $SO(N)$ gauge theories. Some of these dualities have the novel feature that one (anti)fundamental…
We propose matching pairs of half-BPS boundary conditions related by IR dualities of 3d $\mathcal{N}=2$ gauge theories. From these matching pairs we construct duality interfaces. We test our proposals by anomaly matching and the computation…
We propose dualities of $\mathcal{N} = (0,2)$ supersymmetric boundary conditions for 3d $\mathcal{N} = 2$ gauge theories with orthogonal and symplectic gauge groups. We show that the boundary 't Hooft anomalies and half-indices perfectly…
This paper studies $3d$ $\mathcal{N}=4$ 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…
We compute supersymmetric indices to test mirror symmetry of three-dimensional $\mathcal{N}=4$ gauge theories and dualities of half-BPS enriched boundary conditions and interfaces in four-dimensional $\mathcal{N}=4$ Super Yang-Mills theory.…
We find boundary confining dualities of 3d $\mathcal{N}=2$ supersymmetric gauge theories with exceptional gauge groups. The half-indices which enumerate the boundary BPS local operators in the presence of Neumann and Dirichlet boundary…
We present an identity relating the partition function of N=4 supersymmetric QED to that of its dual under mirror symmetry. The identity is a generalized Fourier transform. Many known properties of abelian theories can be derived from this…
We find matching pairs of the line defect indices for 3d supersymmetric Abelian gauge theories as strong evidence of dualities of the BPS line operators. They lead to novel duality maps of the BPS line operators for $\mathcal{N}\ge 4$…
We introduce several families of $\mathcal{N}=(2,2)$ UV boundary conditions in 3d $\mathcal N=4$ gauge theories and study their IR images in sigma-models to the Higgs and Coulomb branches. In the presence of Omega deformations, a UV…
A four-dimensional Abelian gauge field can be coupled to a 3d CFT with a $U(1)$ symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFT) parametrized by the gauge coupling…
We propose a family of IR dualities for 3d $\mathcal{N}=4$ $U(N)$ SQCD with $N_f$ fundamental flavors and $P$ Abelian hypermultiplets i.e. $P$ hypermultiplets in the determinant representation of the gauge group. These theories are good in…
We propose $SL(2,\mathbb{Z})$ dualities of supersymmetric boundary conditions in the three-dimensional supersymmetric field theories describing a semi-infinite M2-brane terminating on M5-branes. Specifically, we present dualities of…
We study boundary conditions in N=4 super Yang-Mills theory that preserve one-half the supersymmetry. The obvious Dirichlet boundary conditions can be modified to allow some of the scalar fields to have a ``pole'' at the boundary. The…
We propose an Abelian mirror dual for the $\mathcal{N}=2$ SQCD$_3$ that we obtain as real mass deformation of known $\mathcal{N}=4$ mirror pairs. We match the superconformal index and the $\mathbf{S}^3_b$ partition function, discuss the…
The half-BPS boundary conditions preserving $\mathcal{N}=(2,2)$ and $\mathcal{N}=(0,4)$ supersymmetry in 3d $\mathcal{N}=4$ supersymmetric gauge theories are examined. The BPS equations admit decomposition of the bulk supermultiplets into…
We analyze the supersymmetric defect indices of $\mathcal{N}=4$ super Yang Mills theories which are simultaneously decorated by the BPS line operators and the boundary conditions. We demonstrate that the two-point functions of the boundary…
This paper presents new developments in the study of 3d mirror symmetry and the phase structure of Abelian gauge theories. Previous works identified 3d mirrors for a specific class of theories, termed ``simple" Abelian theories. This work…
We clarify how mirror symmetry acts on 3d theories with N=2,3 or 4 supersymmetries and non-abelian Chern-Simons terms and then construct many new examples. We identify a new duality, geometric duality, that allows us to generate large…
We propose a new class of infrared dualities relating three-dimensional $\mathcal{N}=2$ $USp(2N)$ Chern--Simons SQCD to planar Abelian quiver gauge theories. These dual descriptions are constructed via real mass deformations of established…