Related papers: Surfaces associated with sigma models and the sine…
This is a review aimed at a physics audience on the relation between Poisson sigma models on surfaces with boundary and deformation quantization. These models are topological open string theories. In the classical Hamiltonian approach, we…
A class of surfaces-graphs in a Riemannian 3-space with a prescribed projection of one field of principal directions onto a surface $\Pi$ is considered. A problem of determination of such surfaces when both principal curvatures are given…
In this paper, we construct and investigate two supersymmetric versions of the Fokas-Gel'fand formula for the immersion of 2D surfaces associated with a supersymmetric integrable system. The first version involves an infinitesimal…
In the preceding paper, we derived Coulomb-gas and sine-Gordon Hamiltonians to describe the Kosterlitz-Thouless transition on a fluctuating surface. These Hamiltonians contain couplings to Gaussian curvature not found in a rigid flat…
We describe a simple technique for generating solutions to the classical field equations for an arbitrary nonlinear sigma-model minimally coupled to gravity. The technique promotes an arbitrary solution to the coupled Einstein/Klein-Gordon…
We find the novel class of the supersymmetric deformation of the $\mathbb{CP}^{1}$ $\sigma$-model and its equivalence with the generalised chiral Gross-Neveu. This construction allows the use of field-theoretic techniques and particularly…
We compute a Simons' type formula for the stress-energy tensor of biharmonic maps from surfaces. Specializing to Riemannian immersions, we prove several rigidity results for biharmonic CMC surfaces, putting in evidence the influence of the…
The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian…
A few pages in Siegel describe how, starting with a fundamental polygon for a compact Riemann surface, one can construct a symplectic basis of its homology. This note retells that construction, specializing to the case where the surface is…
This study introduces a new unified structural framework for orbifold sigma models that incorporates twisted sectors, singularities, and smooth regions into a single algebraic object. Traditional approaches to orbifold theories often treat…
We study an integrable equation whose solutions define a triad of one-forms describing a surface with Gaussian curvature -1. We identify a local group of diffeomorphisms that preserve these solutions and establish conserved quantities. From…
We consider the topological sigma-model on Riemann surfaces with genus g and h holes, and target space CP1. We calculate the correlation functions of bulk and boundary operators, and study the symmetries of the model and its most general…
This article is an application of the author's paper about a construction method for discrete constant negative Gaussian curvature surfaces, the nonlinear d'Alembert formula. The heart of this formula is the Birkhoff decomposition, and we…
In this paper, we discuss the generalizations of exact supersymmetries present in the supersymmetrized sigma models. These generalizations are made by making the supersymmetric transformation parameter field-dependent. Remarkably, the…
In terms of non-commutative geometry, we show that the $\sigma$--model can be built up by the gauge theory on discrete group $Z_2$. We introduce a constraint in the gauge theory, which lead to the constraint imposed on linear $\sigma$ model…
We revisit the classical aspects of $\mathcal{N}=(2,2)$ supersymmetric sigma models with Hermitian symmetric target spaces, using the so-called Gross-Neveu (first-order GLSM) formalism. We reformulate these models for complex Grassmannians…
The study of 2-dimensional surfaces of constant curvature constitutes a beautiful branch of geometry with well-documented ties to the mathematical physics of integrable systems. A lesser known, but equally fascinating, fact is its…
We construct Grassmann spaces associated with the incidence geometry of regular and tangential subspaces of a symplectic copolar space, show that the underlying metric projective space can be recovered in terms of the corresponding…
A Riemannian geometry of noncommutative n-dimensional surfaces is developed as a first step towards the construction of a consistent noncommutative gravitational theory. Historically, as well, Riemannian geometry was recognized to be the…
We review applications of the sine-Gordon model, the O(3) non-linear sigma model, the U(1) Thirring model, and the O(N) Gross--Neveu model to quasi one-dimensional quantum magnets, Mott insulators, and carbon nanotubes. We focus upon the…