Related papers: A Brief Introduction to Poisson Sigma-Models

We consider four-dimensional gravity coupled to a non-linear sigma model whose scalar manifold is a non-compact geometrically finite surface $\Sigma$ endowed with a Riemannian metric of constant negative curvature. When the space-time is an…

We point out the existence of nonlinear $\sigma$-models on group manifolds which are left symmetric and right Poisson-Lie symmetric. We discuss the corresponding rich T-duality story with particular emphasis on two examples: the anisotropic…

In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential…

In this article we will examine a "generalized topological sigma model." This so-called "generalized topological sigma model" is the M-Theoretic analog of the standard topological sigma model of string theory. We find that the observables…

Gauge theory is the foundation of the particle physics Standard Model (SM). Considering the multiple gauge sectors for one gauge transformation, we study the generalized Abelian and non-Abelian (Yang-Mills theory) gauge theories. We first…

We generalize the formulation of Poisson-Lie T-dual sigma models on manifolds to supermanifolds. In this respect, we formulate 1+1 dimensional string cosmological models on the Lie supergroup C^3 and its dual (A_1,1 + 2A)^0_(1,0,0), which…

The induced two-dimensional topological N=1 supersymmetric sigma model on a differential Poisson manifold M presented in arXiv:1503.05625 is shown to be a special case of the induced Poisson sigma model on the bi-graded supermanifold…

We propose a generalization of the collective field theory hamiltonian, including interactions between the original bosonic collective field $w_0 (z)$ and supplementary fields ${\bar w}_j (z)$ realizing classically a $w_\infty$ algebra. The…

We provide the geometric actions for most general N=1 supergravity in two spacetime dimensions. Our construction implies an extension to arbitrary N. This provides a supersymmetrization of any generalized dilaton gravity theory or of any…

I present in this paper some tools in Symplectic and Poisson Geometry in view of their applications in Geometric mechanics and Mathematical Physics. After a short discussion of the Lagrangian and Hamiltonian formalisms, including the use of…

In this paper we introduce a class of generalized supersymmetric Toda field theories. The theories are labeled by a continuous parameter and have $N=2$ supersymmetry. They include previously known $N=2$ Toda theories as special cases. Using…

We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…

A globalized version of a trace formula for the Poisson Sigma Model on the disk is presented by using its formal global picture in the setting of the Batalin-Vilkovisky formalism. This global construction includes the concept of zero modes.…

Since physical theories employ mathematical models to describe and predict physical phenomena, our knowledge depends on the models available to that end. To increase their scope we present a particular type of simplified models, serial…

To formulate two-dimensional Yang-Mills theory with adjoint matter fields in the large-N limit as classical mechanics, we derive a Poisson algebra for the color-invariant observables involving adjoint matter fields. We showed rigorously in…

In this paper, we are going to construct the classical field theory on the boundary of the embedding of $\mathbb{R} \times S^{1}$ into the manifold $M$ by the Jacobi sigma model. By applying the poissonization procedure and by generalizing…

Poisson-Lie T-duality in N=2 superconformal WZNW models on the real Lie groups is considered. It is shown that Poisson-Lie T-duality is governed by the complexifications of the corresponding real groups endowed with Semenov-Tian-Shansky…

I propound a non-linear generalization of the Poisson equation describing a "medium" in D dimensions with a "dielectric constant" proportional to the field strength to the power D-2. It is the only conformally invariant scalar theory that…

This essay's title is justified by discussing a class of Yang-Mills-type theories of which standard Yang-Mills theories are special cases but which is broad enough to include gravity as a double field theory. We use the framework of…

We investigate a relationship between a particular class of two-dimensional integrable non-linear $\sigma$-models and variations of Hodge structures. Concretely, our aim is to study the classical dynamics of the $\lambda$-deformed $G/G$…