Related papers: Holomorphic Blocks for 3d Non-abelian Partition Fu…
Mirror Symmetry for a large class of three dimensional $\mathcal{N}=4$ supersymmetric gauge theories has a natural explanation in terms of M-theory compactified on a product of $\text{ALE}$ spaces. A pair of such mirror duals can be…
We present a general prescription by which we can systematically compute exact partition functions of five-dimensional supersymmetric theories which arise in Higgs branches of the $T_N$ theory. The theories may be realized by webs of…
We examine a class of N=2 supersymmetric gauge theories in (3+1) dimensions whose Lagrangians are determined by graphs consisting of two building blocks, namely a tri-vertex and a line. A line represents an SU(2) gauge group and a…
We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change,…
Taking the simple examples of an Abelian 1-form gauge theory in two (1 + 1)-dimensions, a 2-form gauge theory in four (3 + 1)-dimensions and a 3-form gauge theory in six (5 + 1)-dimensions of spacetime, we establish that such gauge theories…
There are few known computable examples of non-abelian surface holonomy. In this paper, we give several examples whose structure 2-groups are covering 2-groups and show that the surface holonomies can be computed via a simple formula in…
We apply supersymmetric localization to N=(2,2) gauged linear sigma models on a hemisphere, with boundary conditions, i.e., D-branes, preserving B-type supersymmetries. We explain how to compute the hemisphere partition function for each…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
Starting with a supersymmetric U(N)xU(N) gauge theory built in N=1 superspace, a nonsupersymmetric theory is obtained by ``twisting'' the gauginos into a different representation of the group than the gauge bosons. Despite the fact that…
A mechanism using the position-dependent gauge coupling is proposed to localize non-Abelian gauge fields on domain walls in five-dimensional space-time. Low-energy effective theory posseses a massless vector field, and a mass gap. The…
We perform a systematic study of S-duality for ${\cal N}=2$ supersymmetric non-linear abelian theories on a curved manifold. Localization can be used to compute certain supersymmetric observables in these theories. We point out that…
This is an introductory review to localization techniques in supersymmetric two-dimensional gauge theories. In particular we describe how to construct Lagrangians of N=(2,2) theories on curved spaces, and how to compute their partition…
We formulate a precise holographic duality between an ensemble of 4d $U(1)^g$ Maxwell theories living on a spin four-manifold $M_4$ and an Abelian BF-type 2-form gauge theory of level $N$, summed over all five-manifolds with boundary $M_4$.…
We present a supersymmetric version of Dirac-Born-Infeld (DBI) theory in noncommutative space-time, both for Abelian and non-Abelian gauge groups. We show, using the superfield formalism, that the definition of a certain ordering with…
It is advocated that the superembedding approach is a generic covariant method for the description of superbranes as models of (partial) spontaneous supersymmetry breaking. As an illustration we construct (in the framework of…
In this paper we consider 4d $\mathrm{SU}(N)$ gauge theories with $N+1$ fundamentals, five antifundamentals and a conjugate two index antisymmetric tensor. The model has been shown to be in a mixed phase in the IR, splitting in an…
We generalize a fundamental theorem in higher dimensional value distribution theory about entire curves in subvarieties $X$ of semi-abelian varieties to the situation of the sequences of holomorphic maps from the unit disc into $X$. This…
A surprising connection between N=2 gauge theory instanton partition functions and conformal blocks has been recently proposed. We illustrate through simple examples the generalization to asymptotically free N=2 gauge theories
A new non-Abelian gauge transformation for two-forms is introduced. Construction is based on a fixed map from the spacetime to the loop space which attachs a closed loop to each point of the spacetime. It is argued that this set-up is…
The Gauss law constraint in the Hamiltonian form of the $SU(2)$ gauge theory of gluons is satisfied by any functional of the gauge invariant tensor variable $\phi^{ij} = B^{ia} B^{ja}$. Arguments are given that the tensor $G_{ij} =…