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The purpose of this note is to give a mathematical treatment to the low energy effective theory of the two-dimensional sigma model. Perhaps surprisingly, our low energy effective theory encodes much of the topology and geometry of the target manifold. In particular, we relate the βfunction of our theory to the Ricci curvature of the target, recovering the physical result of Friedan.doi:10.1090/conm/718/14477 fatcat:zcbcf3jb2reqtgjkofbl4pzgwa