N=(0, 2) Deformation of (2, 2) Sigma Models: Geometric Structure, Holomorphic Anomaly and Exact Beta Functions

Abstract

We study N=(0,2) deformed (2,2) two-dimensional sigma models. Such heterotic models were discovered previously on the world sheet of non-Abelian strings supported by certain four-dimensional N=1 theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the beta functions in terms of the anomalous dimensions analogous to the NSVZ beta function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation. The anomalous dimensions are calculated up to two loops implying that one of the beta functions is explicitly known up to three loops. The fixed point in the ratio of the couplings found previously at one loop is not shifted at two loops. We also consider the N=(0,2) supercurrent supermultiplet (the so-called hypercurrent) and its anomalies, as well as the "Konishi anomaly." This gives us another method for finding exact $\beta$ functions. We prove that despite the chiral nature of the models under consideration quantum loops preserve isometries of the target space.

arXiv comment38 pages, 6 figures, minor changes in the text and references, the journal version

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• 3D supergravity from wrapped M5-branes
• Supersymmetric Tools in Yang-Mills Theories at Strong Coupling: the Beginning of a Long Journey
• On Isometry Anomalies in Minimal N=(0,1) and N=(0,2) Sigma Models
• Comments on the NSVZ $\beta$ Functions in Two-dimensional $\mathcal{N}=(0,2)$ Supersymmetric Models
• A few recent developments in 2d (2,2) and (0,2) theories
• Monopole harmonics on ${\mathbb{CP}}^{n-1}$
• Making supersymmetric connected N =(0,2) Sigma Models
• Anomalies of Minimal N=(0, 1) and N=(0, 2) Sigma Models on Homogeneous Spaces
• More on Two-Dimensional $O(N)$ Models with $\mathcal{N}=(0,1)$ Supersymmetry
• On Grassmannian Heterotic Sigma Model
• $\beta$-function of the level-zero Gross-Neveu model
• Heterotically Deformed Sigma Models on the World Sheet of Semilocal Strings in SQED
• Nonperturbative features in the Lie-algebraic Kähler sigma model with fermions