Three Dimensional Nonlinear Sigma Models in the Wilsonian Renormalization Method

We study the UV properties of the three-dimensional ${\cal N}=4$ SUSY nonlinear sigma model whose target space is $T^*(CP^{N-1})$ (the cotangent bundle of $CP^{N-1}$) to higher orders in the 1/N expansion. We calculate the $\beta$-function to next-to-leading order and verify that it has no quantum corrections at leading and next-to-leading orders.

We study a three dimensional conformal field theory in terms of its partition function on arbitrary curved spaces. The large $N$ limit of the nonlinear sigma model at the non-trivial fixed point is shown to be an example of a conformal field theory, using zeta--function regularization. We compute the critical properties of this model in various spaces of constant curvature ($R^2 \times S^1$, $S^1\times S^1 \times R$, $S^2\times R$, $H^2\times R$, $S^1 \times S^1 \times S^1$ a...

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...

Nonlinear sigma models (NLSM) in d=3 have many interesting and non-trivial features, which were explored poorly in contrast with NLSM in d=2 and d=4. We present a few results from our study of the perturbative and non-perturbative properties of three-dimensional (3D) NLSM. i) We have shown that cancellation of ultra-violet (UV) divergences takes place in 3D extended (N=2,4) supersymmetric NLSM in low orders of the 1/n expansion. ii) We consider noncommutative extension of the...

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 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...

We develop superspace techniques to construct general off-shell N=1,2,3,4 superconformal sigma-models in three space-time dimensions. The most general N=3 and N=4 superconformal sigma-models are constructed in terms of N=2 chiral superfields. Several superspace proofs of the folklore statement that N=3 supersymmetry implies N=4 are presented both in the on-shell and off-shell settings. We also elaborate on (super)twistor realisations for (super)manifolds on which the three-di...

We formulate four-dimensional N=2 supersymmetric nonlinear sigma models in N=1 superspace. We show how to add superpotentials consistent with N=2 supersymmetry. We lift our construction to higher-dimensional spacetime and write five-dimensional nonlinear sigma models in N=1 superspace.

We study the renormalization of an N = 1 supersymmetric Lifshitz sigma model in three dimensions. The sigma model exhibits worldvolume anisotropy in space and time around the high-energy z = 2 Lifshitz point, such that the worldvolume is endowed with a foliation structure along a preferred time direction. In curved backgrounds, the target-space geometry is equipped with two distinct metrics, and the interacting sigma model is power-counting renormalizable. At low energies, th...

This talk is based on a recent paper$^{1}$ of ours. In an attempt to understand three-dimensional conformal field theories, we study in detail one such example --the large $N$ limit of the $O(N)$ non-linear sigma model at its non-trivial fixed point -- in the zeta function regularization. We study this on various three-dimensional manifolds of constant curvature of the kind $\Sigma \times R$ ($\Sigma=S^1 \times S^1, S^2, H^2$). This describes a quantum phase transition at zer...