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

A method for quantizing the bidimensional N=2 supersymmetric non-linear sigma model is developed. This method is both covariant under coordinate transformations (concerning the order relevant for calculations) and explicitly N=2 supersymmetric. The OPE of the supercurrent is computed accordingly, including also the dilaton. By imposing the N=2 superconformal algebra the equations for the metric and dilaton are obtained. In particular, they imply that the dilaton is a constant...

The dual of the four dimensional non-linear sigma model is constructed using techniques familiar to string theory. This construction necessitates the introduction of a rank two antisymmetric tensor field whose properties are examined. The physics of the dual theory and that of the original model are compared. As an illustration we study in detail the SU(2) chiral model. We find that the scattering amplitudes of the charged Goldstone bosons in the two theories are in complete ...

Two-dimensional sigma models on superspheres $S^{r-1|2s} \cong OSp(r|2s)/OSp(r - 1|2s)$ are known to flow to weak coupling $g_{\sigma} \to 0$ in the IR when $r - 2s < 2$. Their long-distance properties are described by a free 'Goldstone' conformal field theory (CFT) with $r - 1$ bosonic and $2s$ fermionic degrees of freedom, where the $OSp(r|2s)$ symmetry is spontaneously broken. This behavior is made possible by the lack of unitarity. The purpose of this paper is to study ...

We prove the Chern-Gauss-Bonnet Theorem using sigma models whose source supermanifolds have super dimension 0|2. Along the way we develop machinery for understanding manifold invariants encoded by families of 0|n-dimensional Euclidean field theories and their quantization.

(Minor corrections and reference added)

The Supersymmetric Dual Sigma Model (SDSM) is a local field theory introduced to be nonlocally equivalent to the Supersymmetric Chiral nonlinear sigma-Model (SCM), this dual equivalence being proven by explicit canonical transformation in tangent space. This model is here reconstructed in superspace and identified as a chiral-entwined supersymmetrization of the Dual Sigma Model (DSM). This analysis sheds light on the Boson-Fermion Symphysis of the dual transition, and on the ...

Supersymmetric quantum mechanical models are computed by the Path integral approach. In the $\beta\rightarrow0$ limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants...

The purpose of this work is to present some basic concepts about the non-linear sigma model in a simple and direct way. We start with showing the bosonic model and the Wess-Zumino-Witten term, making some comments about its topological nature, and its association with the torsion. It is also shown that to cancel the quantum conformal anomaly the model should obey the Einstein equations. We provide a quick introduction about supersymmetry in chapter 2 to help the understanding...

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 model. We present a manifest N=1 off-shell formulation. The analysis is greatly simplified compared to previous studies and there is no need to introduce non-local superspaces nor to go (partially) on-shell. Whether or not torsion is presen...

We consider two-dimensional $\mathcal{N}=(0,2)$ sigma models with the CP(1) target space. A minimal model of this type has one left-handed fermion. Nonminimal extensions contain, in addition, $N_f$ right-handed fermions. Our task is to derive expressions for the $\beta$ functions valid to all orders. To this end we use a variety of methods: (i) perturbative analysis; (ii) instanton calculus; (iii) analysis of the supercurrent supermultiplet (the so-called hypercurrent) and it...