Lie-algebraic K\"ahler sigma models with the U(1) isotropy

In this paper we study the integrability of a family of models with U(1)xSU(N) symmetry. They admit fermionic and bosonic formulations related through bosonization and subsequent T-duality. The fermionic theory is just the CP^(N-1) sigma model coupled to a self-interacting massless fermion, while the bosonic one defines a one-parameter deformation of the O(2N) sigma model. For N=2 the latter model is equivalent to the integrable deformation of the O(4) sigma model discovered ...

We review N=(2,2) supersymmetric non-linear sigma-models in two dimensions and their relation to generalized Kahler and Calabi-Yau geometry. We illustrate this with an explicit non-trivial example.

In this paper we begin the study of renormalizations in the heterotically deformed N=(0,2) CP(N-1) sigma models. In addition to the coupling constant g^2 of the undeformed N=(2,2) model, there is the second coupling constant \gamma describing the strength of the heterotic deformation. We calculate both \beta functions, \beta_g and \beta_\gamma at one loop, determining the flow of g^2 and \gamma. Under a certain choice of the initial conditions, the theory is asymptotically fr...

We review non-linear sigma-models with (2,1) and (2,2) supersymmetry. We focus on off-shell closure of the supersymmetry algebra and give a complete list of (2,2) superfields. We provide evidence to support the conjecture that all N=(2,2) non-linear sigma-models can be described by these fields. This in its turn leads to interesting consequences about the geometry of the target manifolds. One immediate corollary of this conjecture is the existence of a potential for hyper-Kah...

In this paper we examine analytically the large-$N$ gap equation and its solution for the $2D$ $\mathbb{CP}^{N-1}$ sigma model defined on a Euclidean spacetime torus of arbitrary shape and size ($L, \beta)$, $\beta$ being the inverse temperature. We find that the system has a unique homogeneous phase, with the $\mathbb{CP}^{N-1}$ fields $n_i$ acquiring a dynamically generated mass $\langle\lambda\rangle\ge\Lambda^2$ (analogous to the mass gap of $SU(N)$ Yang-Mills theory in $...

We consider the N=1 supersymmetric two-dimensional non-linear sigma model with boundaries and nonzero B-field. By analysing the appropriate currents we describe the full set of boundary conditions compatible with N=1 superconformal symmetry. Using this result the problem of finding a correct action is discussed. We interpret the supersymmetric boundary conditions as a maximal integral submanifold of the target space manifold, and speculate about a new geometrical structure, t...

Two-dimensional (2,2) supersymmetric nonlinear sigma models can be described in (2,2), (2,1) or (1,1) superspaces. Each description emphasizes different aspects of generalized K\"ahler geometry. We investigate the reduction from (2,2) to (2,1) superspace. This has some interesting nontrivial features arising from the elimination of nondynamical fields. We compare quantization in the different superspace formulations.

We consider supersymmetric sigma models on the Kahler target spaces, with twisted mass. The Kahler spaces are assumed to have holomorphic Killing vectors. Introduction of a superpotential of a special type is known to be consistent with N=2 superalgebra (Alvarez-Gaume and Freedman). We show that the algebra acquires central charges in the anticommutators {Q_L, Q_L} and {Q_R, Q_R}. These central charges have no parallels, and they can exist only in two dimensions. The central ...

We present two examples of SUSY mechanics related with K\"ahler geometry. The first system is the N=4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N=2 SUSY mechanics whose phase space is the external algebra of an arbitrary K\"ahler manifold. The relation of these models with antisymplectic geometry is discussed.

We revisit supersymmetric nonlinear sigma models on the target manifold $CP^{N-1}$ and $SO(N)/SO(N-2)\times U(1)$ in four dimensions. These models are formulated as gauged linear models, but it is indicated that the Wess-Zumino term should be added to the linear model since the hidden local symmetry is anomalous. Applying a procedure used for quantization of anomalous gauge theories to the nonlinear models, we determine the form of the Wess-Zumino term, by which a global symm...