N=(0,2) Deformation of CP(1) Model: Two-dimensional Analog of N=1 Yang-Mills Theory in Four Dimensions

Abstract

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 its anomalies, and some other arguments. All these arguments, combined, indicate a direct parallel between the heterotic $\mathcal{N}=(0,2)$ CP(1) models and four-dimensional super-Yang-Mills theories. In particular, the minimal $\mathcal{N}=(0,2)$ CP(1) model is similar to $\mathcal{N}=1$ supersymmetric gluodynamics. Its exact $\beta$ function can be found; it has the structure of the Novikov-Shifman-Vainshtein-Zakharov (NSVZ) $\beta$ function of supersymmetric gluodynamics. The passage to nonminimal $\mathcal{N}=(0,2)$ sigma models is equivalent to adding matter. In this case an NSVZ-type exact relation between the $\beta$ function and the anomalous dimensions $\gamma$ of the "matter" fields is established. We derive an analog of the Konishi anomaly. At large $N_f$ our $\beta$ function develops an infrared fixed point at small values of the coupling constant (analogous to the Banks-Zaks fixed point). Thus, we reliably predict the existence of a conformal window. At $N_f=1$ the model under consideration reduces to the well-known $\mathcal{N}=(2,2)$ CP(1) model.

arXiv comment31 pages, 6 figures; a typo in the previous arXiv version was corrected, the current version is compatible with the published version

References in corpus (19)

• Vortices, Instantons and Branes
• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• Solitons in the Higgs phase -- the moduli matrix approach --
• Vortex Strings and Four-Dimensional Gauge Dynamics
• Non-Abelian String Junctions as Confined Monopoles
• R-Twisting and 4d/2d Correspondences
• Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity
• Holomorphy, Rescaling Anomalies and Exact beta Functions in Supersymmetric Gauge Theories
• Quantum Vortex Strings: A Review
• Supercurrents and Brane Currents in Diverse Dimensions
• Heterotic Vortex Strings
• Quantization of Integrable Systems and a 2d/4d Duality
• Heterotic Flux Tubes in N=2 SQCD with N=1 Preserving Deformations
• The BPS Spectra of Two-Dimensional Supersymmetric Gauge Theories with Twisted Mass Terms
• The Magnetic Monopole Seventy-Five Years Later
• Chiral Algebras of (0,2) Sigma Models: Beyond Perturbation Theory - II
• Chiral Algebras of (0,2) Sigma Models: Beyond Perturbation Theory
• N=(0,2) Supersymmetry and a Nonrenormalization Theorem
• Perturbative Aspects of Heterotically Deformed CP(N-1) Sigma Model. I

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• Peculiarities of beta functions in sigma models
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• Degenerate kinks and kink-instantons in two-dimensional scalar field models with $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry
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