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A gauge theory with 4 physical dimensions can be consistently expressed as a renormalizable topological quantum field theory in 5 dimensions. We extend the symmetries in the 5-dimensional framework to include not only a topological BRST…

We show that a large subclass of 3d $\mathcal{N}=4$ quiver gauge theories consisting of unitary and special unitary gauge nodes with only fundamental/bifundamental matter have multiple Seiberg-like IR duals. A generic quiver $\mathcal{T}$…

We use the language of von Neumann subfactors to investigate non-invertible symmetries in two dimensions. A fusion categorical symmetry $\mathcal{C}$, its module category $\mathcal{M}$, and a gauging labeled by an algebra object…

We construct rigid supersymmetric gauge theories on Riemannian five-manifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of a six-dimensional bulk supergravity solution. This leads to a systematic…

Let $Gr(d,n)$ be the Grassmannian of $d$-dimensional linear subspaces of an $n$-dimensional vector space $V$. A submanifold $X\subset Gr(d, n)$ gives rise to a differential system $\Sigma(X)$ that governs $d$-dimensional submanifolds of $V$…

We study $N=5$ gauged supergravity in three dimensions with compact, non-compact and non-semisimple gauge groups. The theory under consideration is of Chern-Simons type with $USp(4,k)/USp(4)\times USp(k)$ scalar manifold. We classify…

We present a new family of dualities for three-dimensional gauge theories, motivated by the brane realization of the reduction of four-dimensional dualities on a circle. This family can be understood as a generalization of Aharony duality…

We study several cases of IR enhancements of global symmetry in four dimensions. In particular, we consider a sequence of $Spin(n+4)$ supersymmetric gauge theories ($8\geq n\geq 1$) with $n$ vectors and spinor matter with $32$ components.…

We determine the higher symmetries of 5d SCFTs engineered from M-theory on a $\mathbb{C}^3 / \Gamma$ background for $\Gamma$ a finite subgroup of $SU(3)$. This resolves a longstanding question as to how to extract this data when the…

The zero-form and one-form global symmetries of the Aharony-Bergman-Jafferis (ABJ) and related theories, with at least $\mathcal{N}=6$ supersymmetry in three dimensions, are examined in detail. Starting from well-known dualities between…

We study the relation between class S theories on punctured tori and isomonodromic deformations of flat SL(N) connections on the two dimensional torus with punctures. Turning on the self dual $\Omega$-background corresponds to a…

This work has its origins in an attempt to describe systematically the integrable geometries and gauge theories in dimensions one to four related to twistor theory. In each such dimension, there is a nondegenerate integrable geometric…

We derive integrable discrete systems which are contiguity relations of two equations in the Painlev\'e-Gambier classification depending on some parameter. These studies extend earlier work where the contiguity relations for the six…

We study the general gaugings of N=2 Maxwell-Einstein supergravity theories (MESGT) in five dimensions, extending and generalizing previous work. The global symmetries of these theories are of the form SU(2)_R X G, where SU(2)_R is the…

The classification of 1/4-supersymmetric solutions of five dimensional gauged supergravity coupled to arbitrary many abelian vector multiplets, which was initiated in hep-th/0401129, is completed. The structure of all solutions for which…

We report on numerical simulations of one dimensional maximally supersymmetric SU(N) Yang-Mills theory, by using the lattice action with two exact supercharges. Based on the gauge/gravity duality, the gauge theory corresponds to N D0-branes…

We construct new half-BPS line defects in 3d $\mathcal{N}=2$ supersymmetric quiver gauge theories whose Higgs branches are complete flag manifolds $X = {\rm Fl}(n)$. Upon circle compactification, the bulk theory flows to a non-linear sigma…

We investigate the symmetry structure of five-dimensional Yang-Mills theories with $\mathfrak{su}(N)$ gauge algebra. These theories feature intertwined 0-, 1-, and 2-form symmetries, depending on the global variant one is considering. In…

A new class of models of dynamical supersymmetry breaking is proposed. The models are based on SU(N_C) gauge theories with N_F(<N_C) flavors of quarks and singlets. Dynamically generated superpotential exibits runaway behavior. By embedding…

We study gauging interfaces and their defect descendants in lattice models with generalized symmetries in higher dimensions. We construct explicit interface Hamiltonians for gauging a $\mathbb Z_2^{(0)}$ symmetry in $(2+1)d$ and a $\mathbb…