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.

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

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Cited by in corpus (5)

• 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
• Making supersymmetric connected N =(0,2) Sigma Models
• On Grassmannian Heterotic Sigma Model
• Heterotically Deformed Sigma Models on the World Sheet of Semilocal Strings in SQED