Related papers: Uses of Sigma Models

Nonlinear sigma models (NLSM) in d=3 have many interesting and non-trivial features, which were explored poorly in contrast with NLSM in d=2 and d=4. We present a few results from our study of the perturbative and non-perturbative…

We treat in this paper non-linear sigma models such as $CP^1$-model, $QP^1$-model and etc, in 1+2 dimensions. For submodels of such ones we definitely construct an infinite number of nontrivial conserved currents. Our result is a…

Explicit solutions to the conifold equations with complex dimension $n=3,4$ in terms of {\it{complex coordinates (fields)}} are employed to construct the Ricci-flat K\"{a}hler metrics on these manifolds. The K\"{a}hler 2-forms are found to…

We construct on-shell ${\mathcal{N}}=2$ nonlinear sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ by holomorphically embedding the models in the hyper-K\"{a}hler nonlinear sigma model on the cotangent bundle of the Grassmann manifold $T^\ast…

Noncommutative geometry has seen remarkable applications for high energy physics, viz. the geometrical interpretation of the Standard Model. The question whether it also allows for supersymmetric theories has so far not been answered in a…

General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…

In this paper we construct topological sigma models which include a potential and are related to twisted massive supersymmetric sigma models. Contrary to a previous construction these models have no central charge and do not require the…

We describe the conditions for extra supersymmetry in N=(2,2) supersymmetric nonlinear sigma models written in terms of semichiral superfields. We find that some of these models have additional off-shell supersymmetry. The (4,4)…

A particular form of non-linear $\sigma$-model, having a global gauge invariance, is studied. The detailed discussion on current algebra structures reveals the non-abelian nature of the invariance, with {\it{field dependent structure…

The equivalence between rank-2 anti-symmetric tensor fields, considered as gauge potentials, and torsionless non-linear $\sigma$-models suggests us to study the possibility of coupling tensorial matter with Yang-Mills fields, through the…

For the most general off-shell N = 2 supersymmetric sigma model in projective superspace, we elaborate on its formulation in terms of N = 1 chiral superfields. A universal (model-independent) expression is obtained for the holomorphic…

We propose an integrable extension of nonlinear sigma model on the target space of Hermitian symmetric space (HSS). Starting from a discussion of soliton solutions of O(3) model and an integrally extended version of it, we construct general…

Kahler manifolds have a natural hyperkahler structure associated with (part of) their cotangent bundles. Using projective superspace, we construct four-dimensional N = 2 models on the tangent bundles of some classical Hermitian symmetric…

We have developed N=1 supersymmetric nonlinear realization methods, which realize global symmetry breaking in N=1 supersymmetric theories. The target space of nonlinear sigma models with a linear model origin is a G^C-orbit, which is a…

This set of lectures contain a brief review of some basic supersymmetry and its representations, with emphasis on superspace and superfields. Starting from the Poincar\'e group, the supersymmetric extensions allowed by the Coleman-Mandula…

We study non-linear $\sigma$-models defined on noncommutative torus as a two dimensional string world-sheet. We consider a quantum group as a noncommutative space-time as well as two points, a circle, and a noncommutative torus. Using the…

After an elementary presentation of the relation between supersymmetric nonlinear sigma models and geometry, I focus on 2D and the target space geometry allowed when there is an extra supersymmetry. This leads to a brief introduction to…

An introduction is given to some selected aspects of noncommutative geometry. Simple examples in this context are provided by finite sets and lattices. As an application, it is explained how the nonlinear Toda lattice and a discrete time…

Harmonic maps from Riemann surfaces arise from a conformally invariant variational problem. Therefore, on one hand, they are intimately connected with moduli spaces of Riemann surfaces, and on the other hand, because the conformal group is…

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…