Related papers: The Poisson sigma model on closed surfaces
We examine the structure of lower-dimensional standard model vacua for two-dimensional compactifications (on a 2D torus and on a 2D sphere). In the case of the torus we find a new standard model vacuum for a large range of neutrino masses…
The Minimal Linear $\sigma$ Model is a useful theoretical laboratory. One can investigate in a perturbative renormalisable model the properties of the Higgs boson as a pseudo-Goldstone boson, the phenomenological effects of the radial mode…
We construct a Chern-Simons action for q-deformed gauge theory which is a simple and straightforward generalization of the usual one. Space-time continues to be an ordinary (commuting) manifold, while the gauge potentials and the field…
A remarkable theoretical prediction for a crystalline (polymerized) surface is that its Poisson ratio (\sigma) is negative. Using a large scale Monte Carlo simulation of a simple model of such surfaces we show that this is indeed true. The…
Quadratic Poisson tensors of the Dufour-Haraki classification read as a sum of an $r$-matrix induced structure twisted by a (small) compatible exact quadratic tensor. An appropriate bigrading of the space of formal Poisson cochains then…
We employ cut and paste contact topological techniques to classify some tight contact structures on the closed, oriented genus-2 surface times the interval. A boundary condition is specified so that the Euler class of the of the contact…
We introduce C-Algebras of compact Riemann surfaces $\Sigma$ as non-commutative analogues of the Poisson algebra of smooth functions on $\Sigma$. Representations of these algebras give rise to sequences of matrix-algebras for which…
We study deformations of symplectic structures on a smooth manifold $M$ via the quasi-Poisson theory. By a fact, we can deform a given symplectic structure $\omega $ to a new symplectic structure $\omega_t$ parametrized by some element $t$…
The main result of this paper is a Pfaffian formula for the partition function of the dimer model on a graph G embedded in a closed, possibly non-orientable surface S. This formula is suitable for computational purposes, and it is obtained…
In Batalin-Vilkovisky formalism a classical mechanical system is specified by means of a solution to the {\sl classical master equation}. Geometrically such a solution can be considered as a $QP$-manifold, i.e. a super\m equipped with an…
Jacobi sigma models are two-dimensional topological non-linear field theories which are associated with Jacobi structures. The latter can be considered as a generalization of Poisson structures. After reviewing the main properties and…
The closedness of orbits of central forces is addressed in a three dimensional space in which the Poisson bracket among the coordinates is that of the SU(2) Lie algebra. In particular it is shown that among problems with spherically…
This monograph explores classification and perturbation problems for integrable systems on a class of Poisson manifolds called $b^m$-Poisson manifolds. Even if the class of $b^m$-Poisson manifolds is not ample enough to represent general…
We introduce K-deformations of generalized complex structures on a compact Kahler manifold $M=(X, J)$ with an effective anti-canonical divisor and show that obstructions to K-deformations of generalized complex structures on $M$ always…
In this note we study numerically the combinatorics of curves and geodesics on the torus with one boundary component. A potential computational difficulty is avoided by counting inside specific orbits of the mapping class group up to a…
We discuss the existence of equilibrium configurations for the Hamiltonian point-vortex model on a closed surface $\Sigma$. The topological properties of $\Sigma$ determine the occurrence of three distinct situations, corresponding to…
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…
In this paper we address two questions concerning the effective action of a topological insulator in one and three dimensional space without boundaries, such as a torus. The first is whether a uniform $\theta$-term with $\theta=\pi$ is…
Recently de Thanhoffer de V\"olcsey and Van den Bergh classified the Euler forms on a free abelian group of rank 4 having the properties of the Euler form of a smooth projective surface. There are two types of solutions: one corresponding…
We study the Hochschild cohomology and the Gerstenhaber algebra structure on the algebraic non-commutative torus/quantum torus orbifolds resulting by the action of finite subgroups of $SL_2(\mathbb Z)$. We also examine the Poisson…