Séminaire de Physique Théorique

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

by Prof. Misha SHIFMAN (University of Minesota & IHÉS)

Centre de conférences Marilyn et James Simons (IHES)

Centre de conférences Marilyn et James Simons


IHES Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
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. We prove that despite the chiral nature of the model anomalies in the isometry currents do not appear for CP(N-1) at any N. This is in contradistinction with the minimal heterotic model (with no right-moving fermions) which is anomaly-free only for N=2, i.e. in CP(1). 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 β functions. A clear–cut parallel between N=1 4D Yang-Mills and N=(0,2) 2D sigma models is revealed.