Related papers: Noncommutative Nonlinear Sigma Models and Integrab…

The conditions under which a general two-dimensional non-linear sigma model is classically integrable are given. These requirements are found by demanding that the equations of motion of the theory are expressible as a zero curvature…

Chiral symmetry provides the symmetry protection for a large class of topological edge states. It exists in non-Hermitian systems as well, and the same anti-commutation relation between the Hamiltonian and a linear chiral operator, i.e.,…

We show that the action functional of the nonlinear sigma model with gravitino considered in a previous article [18] is invariant under rescaled conformal transformations, super Weyl transformations and diffeomorphisms. We give a careful…

At large N_c, cold nuclear matter is expected to form a crystal and thus spontaneously break translational symmetry. The description of chiral symmetry breaking and translational symmetry breaking can become intertwined. Here, the focus is…

We consider a class of sigma models that appears from a generalisation of the gauged WZW model parametrised by a constant matrix $Q$. Particular values of $Q$ correspond to the standard gauged WZW models, chiral gauged WZW models and a…

Four different extensions of the Standard Model to non-commutative space-time are considered. They all have the structure group U_Y(1) x SU_L(2) x SU_c(3) but differ through the way Yukawa interaction is implemented. Models based on…

It is commonly asserted that there is a \hat G\times G centreless Kac-Moody extension of the manifest G\times G global symmetry of the two-dimensional principal chiral model (PCM) for the group manifold G. Here, we show that the symmetry is…

The large-$N$ nonlinear $O(N)$, $CP^{N-1}$ $\sigma$ models are studied on $R^2 \times S^1$. The $N$-components scalar fields of the models are supposed to acquire a phase $e^{i2\pi\delta}$ $(0\leq \delta <1)$, along the circulation of the…

We consider a four dimensional generalized Wess-Zumino model formulated in terms of an arbitrary K\"{a}hler potential $\mathcal{K}(\Phi,\bar{\Phi})$ and an arbitrary chiral superpotential $\mathcal{W}(\Phi)$. A general analysis is given to…

Calogero-Sutherland models of $N$ identical particles on a circle are deformed away from hermiticity but retaining a $\cal PT$ symmetry. The interaction potential gets completely regularized, which adds to the energy spectrum an infinite…

We study two-dimensional supersymmetric non-linear sigma-models with boundaries. We derive the most general family of boundary conditions in the non-supersymmetric case. Next we show that no further conditions arise when passing to the N=1…

Following arXiv:1907.04737, we continue our investigation of the relation between the renormalizability (with finitely many couplings) and integrability in 2d $\sigma$-models. We focus on the "$\lambda$-model," an integrable model…

We initiate a study of projections and modules over a noncommutative cylinder, a simple example of a noncompact noncommutative manifold. Since its algebraic structure turns out to have many similarities with the noncommutative torus, one…

In this paper we give the first examples of positive closed currents in $\mathbb{C}^2$ with continuous potentials, vanishing self-intersection, and which are not laminar. More precisely, they are supported on sets "without analytic…

We study the CP(1) system in (2+1)-dimensional noncommutative space with and without Chern-Simons term. Using the Seiberg-Witten map we convert the noncommutative CP(1) system to an action written in terms of the commutative fields. We find…

We extend the investigation of three-dimensional (3D) Hamiltonian systems of non-subgroup type admitting non-zero magnetic fields and an axial symmetry, namely the circular parabolic case, the oblate spheroidal case and the prolate…

We introduce a Hodge operator in a framework of noncommutative geometry. The complete integrability of 2-dimensional classical harmonic maps into groups (sigma-models or principal chiral models) is then extended to a class of…

This is a challenging paper including some review and new results. Since the non-commutative version of the classical system based on the compact group SU(2) has been constructed in (quant-ph/0502174) by making use of Jaynes-Commings model…

We offer a simple non-perturbative formula for the component action of a generic N=1/2 supersymmetric chiral model in terms of an arbitrary number of chiral superfields in four dimensions, which is obtained by the Non-Anti-Commutative (NAC)…

We study the instanton equation of the supersymmetric CP^{N-1} sigma model on non(anti)commutative superspace in two dimensions. We show that the undeformed instanton equation is consistent with the deformed equations of motion. Then we…