Two-Dimensional Models With (0,2) Supersymmetry: Perturbative Aspects

In this paper, we study the RG flow in the non-linear sigma models obtained from a 2d N=(0,2) supersymmetric QCD. The sigma model is parameterized by a single Kahler modulus. We determine its exact non-perturbative beta function using holomorphy, triality and the knowledge of the infra-red fixed point.

In this paper we compute spaces of chiral operators in general two-dimensional (0,2) nonlinear sigma models, both in theories twistable to the A/2 or B/2 model, as well as in non-twistable theories, and apply them to check recent duality conjectures. The fact that in a nonlinear sigma model, the Fock vacuum can act as a section of a line bundle on the target space plays a crucial role in our (0,2) computations, so we begin with a review of this property. We also take this opp...

We discuss the ultra-violet properties of bosonic and supersymmetric noncommutative non-linear sigma-models in two dimensions, both with and without a Wess-Zumino-Witten term.

We extend our analysis in [arXiv:0801.4782] and show that the chiral algebras of (0,2) sigma models are totally trivialized by worldsheet instantons for all complete flag manifolds of compact semisimple Lie groups. Consequently, supersymmetry is spontaneously broken. Our results verify Stolz's idea that there are no harmonic spinors on the loop spaces of these flag manifolds. Moreover, they also imply that the kernels of certain twisted Dirac operators on these spaces will be...

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.

We consider a general N=(2,2) non-linear sigma-model in (2,2) superspace. Depending on the details of the complex structures involved, an off-shell description can be given in terms of chiral, twisted chiral and semi-chiral superfields. Using superspace techniques, we derive the conditions the potential has to satisfy in order to be ultra-violet finite at one loop. We pay particular attention to the effects due to the presence of semi-chiral superfields. A complete descriptio...

Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy are characterized by symmetries related to covariantly constant forms that these manifolds hold, which are generally non-linear and close in a field dependent sense. The thesis explores various aspects of the special holonomy symmetries.

The NSVZ $\beta$ functions in two-dimensional $\mathcal N=(0,2)$ supersymmetric models are revisited. We construct and discuss a broad class of such models using the gauge formulation. All of them represent direct analogs of four-dimensional ${\mathcal N} =1$ Yang-Mills theories and are free of anomalies. Following the same line of reasoning as in four dimensions we distinguish between the holomorphic and canonical coupling constants. This allows us to derive the exact two-di...

In this work, we analyze an extended $\mathcal{N}=2$ supersymmetry with central charge and develop its superspace formulation under two distinct viewpoints. Initially, in the context of classical mechanics, we discuss the introduction of deformed supersymmetric derivatives and their consequence on the deformation of one-dimensional non-linear sigma model. After that, considering a field-theoretical framework, we present an implementation of this superalgebra in two dimensions...

We consider two dimensional non linear sigma models on few symmetric superspaces, which are supergroup manifolds of coset type. For those spaces where one loop beta function vanishes, two loop beta function is calculated and is shown to be zero. Vanishing of beta function in all orders of perturbation theory is shown for the principal chiral models on group supermanifolds with zero Killing form. Sigma models on symmetric (super) spaces on supergroup manifold $G/H$ are known t...