On a class of finite sigma-models and string vacua; a supersymmetric extension

This article studies some features of quantum field theories with internal supersymmetry, focusing mainly on 2-dimensional non-linear sigma models which take values in a coset superspace. It is discussed how BRST operators from the target space supersymmetry algebra can be used to identify subsectors which are often simpler than the original model and may allow for an explicit computation of correlation functions. After an extensive discussion of the general reduction scheme,...

In this paper we consider perturbation theory in generic two-dimensional sigma models in the so-called first-order formalism, using the coordinate regularization approach. Our goal is to analyze the first-order formalism in application to $\beta$ functions and compare its results with the standard geometric calculations. Already in the second loop, we observe deviations from the geometric results that cannot be explained by the regularization/renormalization scheme choices. M...

We study the non-linear sigma model realization of a heterotic vacuum with N=2 space-time supersymmetry. We examine the requirements of (0,2) + (0,4) world-sheet supersymmetry and show that a geometric vacuum must be described by a principal two-torus bundle over a K3 manifold.

We study D-branes of N=2 supersymmetric sigma models. Supersymmetric nonlinear sigma models with 2-dimensional target space have D0,D1,D2-branes, which are realized as A-,B-type supersymmetric boundary conditions on the worldsheet. When we embed the models in the string theory, the Kahler potential is restricted and leads to a 2-dim black hole metric with a dilaton background. The D-branes in this model are susy cycles and consistent with the analysis of conjugacy classes. Th...

We present a systematic study of ${\cal N}=(2,2)$ supersymmetric non-linear sigma models on $S^2$ with the target being a K\"ahler manifold. We discuss their reformulation in terms of cohomological field theory. In the cohomological formulation we use a novel version of 2D self-duality which involves a $U(1)$ action on $S^2$. In addition to the generic model we discuss the theory with target space equivariance corresponding to a supersymmetric sigma model coupled to a non-dyn...

We propose a class of N=2 supersymmetric nonlinear sigma models on the Ricci-flat Kahler manifolds with O(n) symmetry.

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 generalized complex geometry, a notion introduced recently by Hitchin which interpolates between complex and symplectic manifolds. Finally I present worldsheet realizations of this geometry,

We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it generally decomposes into two separate quaternionic spaces, associated with inequivalent supermultiplets. For N=5,6,8 there is a unique (symmetric) space for any given number of supermult...

We extend the results of hep-th/0310137 to show that a general classical action for D=2, N=2 sigma models on a non(anti)commutative superspace is not standard and contains infinite number of terms, which depend on the determinant of the non(anti)commutativity parameter, C^{\alpha\beta}. We show that using Kahler normal coordinates the action can be written in a manifestly covariant manner. We introduce vector multiplets and obtain the N=1/2 supersymmetry transformations of th...

We discuss various questions which emerge in connection with the Lie-algebraic deformation of $\mathbb{CP}^1$ sigma model in two dimensions. First we supersymmetrize the original model endowing it with the minimal ${\cal N}=(0,2)$ and extended ${\cal N}=(2,2)$ supersymmetries. Then we derive the general hypercurrent anomaly in the both cases. In the latter case this anomaly is one-loop but is somewhat different from the standard expressions one can find in the literature beca...