Related papers: 3D Bosons and $W_{1+\infty}$ algebra

Recently, the {\it spacelike} part of the $SU(2)$ Yang--Mills equations has been identified with geometrical objects of a three--dimensional space of constant Riemann--Cartan curvature. We give a concise derivation of this Ashtekar type…

A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of…

Bosonization of the gauged, massive Thirring model in 2+1-dimensions produces a Maxwell-Chern-Simons gauge theory, coupled to a dynamical, massive vector field. Exploiting the Master Lagrangian formalism, two dual theories are constructed,…

The complex geometry of the Ly$\alpha$ forest data has motivated the use of various two-point statistics as alternatives to the three-dimensional power spectrum ($P_{\mathrm{3D}}$), which carries cosmological information in Fourier space.…

Dimer models have been used in string theory to construct path algebras with relations that are 3-dimensional Calabi-Yau Algebras. These constructions result in algebras that share some specific properties: they are finitely generated…

We shall interpret the null hexagonal Wilson loop (or, equivalently, six gluon scattering amplitude) in 4D ${\cal N}=4$ Super Yang-Mills, or, precisely, an integral representation of its matrix part, via an ADHM-like instanton construction.…

We construct the classical Poisson structure and $r$-matrix for some finite dimensional integrable Hamiltonian systems obtained by constraining the flows of soliton equations in a certain way. This approach allows one to produce new kinds…

Let $\D$ be the Lie algebra of regular differentialoperators on ${\C} \setminus \{0\}$, and ${\hD}= {\D} + {\C} C$ be the central extension of ${\D}$. Let $W_{1+\infty,-N}$ be the vertex algebra associated to the irreducible vacuum…

It was recently shown that charged AdS boson stars can reproduce the universal structure of the lowest scaling dimension in the subsector of a CFT with fixed large global $U(1)$ charge $Q$. Using the model consisting of Einstein-Maxwell…

We present three Lagrangian algebras in the modular 2-category associated to the 3+1D $\mathbb{Z}_2$ topological order and discuss their physical interpretations, connecting algebras with gapped boundary conditions, and interestingly, maps…

We compute the partition function on S^3 of 3d N=4 theories which arise as the low-energy limit of 4d N=4 super Yang-Mills theory on a segment or on a junction, and propose its 1d interpretation. We show that the partition function can be…

We introduce a family of area preserving generalized baker's transformations acting on the unit square and having sharp polynomial rates of mixing for Holder data. The construction is geometric, relying on the graph of a single variable…

We calculate Wilson loops in lowest order of perturbation theory for triangular contours whose edges are circular arcs. Based on a suitable disentanglement of the relations between metrical and conformal parameters of the contours, the…

Using the concept of 3-Lie bialgebra, which has recently been defined in arXiv:1604.04475, we construct Bagger-Lambert-Gustavson (BLG) model for M2-brane on Manin triple of a special 3-Lie bialgebra. Then by using the correspondence and…

The aim of this paper is to establish necessary and sufficient algorithmic conditions to guarantee that an algebra is actually a 3-dimensional skew polynomial algebra in the sense of Bell and Smith.

In this study, we introduce a new class of rational elliptic 3-folds, which we refer to as "1/2 Calabi-Yau 3-folds". We construct elliptically fibered Calabi-Yau 3-folds by utilizing these rational elliptic 3-folds. The construction yields…

The Relativistic formulation of the three-boson model interacting via a zero-range two-body force in the null-plane is given in 2+1 and 1+1 space-time dimension. The bound state energy is calculed as function of the two-body boson binding…

We introduce $3d$ printing, a new algorithm for generating $2d$ $\mathcal{N}=(0, 2)$ gauge theories on D1-branes probing singular toric Calabi-Yau 4-folds using $4d$ $\mathcal{N}=1$ gauge theories on D3-branes probing toric Calabi-Yau…

The Sp(2)-gauge fixing of N = 1 super-Yang-Mills theory is considered here. We thereby apply the triplectic scheme, where two classes of gauge-fixing bosons are introduced. The first one depends only on the gauge field, whereas the second…

We show that the 2d Poisson Sigma Model on a Poisson groupoid arises as an effective theory of the 3d Courant Sigma Model associated to the double of the underlying Lie bialgebroid. This field-theoretic result follows from a Lie-theoretic…