Exact Results for Supersymmetric Sigma Models

Details Exact Results for Supersymmetric Sigma Models Exact Results for Supersymmetric Sigma Models

1991-11-07

arxiv.org/abs/hep-th/9111016v1

Phys.Rev.Lett. 68 (1992) 903-906

Physics

High Energy Physics

High Energy Physics - Theory

9 p

Scientific paper

10.1103/PhysRevLett.68.903

We show that the metric and Berry's curvature for the ground states of $N=2$ supersymmetric sigma models can be computed exactly as one varies the Kahler structure. For the case of $CP^n$ these are related to special solutions of affine toda equations. This allows us to extract exact results (including exact instanton corrections). We find that the ground state metric is non-singular as the size of the manifold shrinks to zero thus suggesting that 2d QFT makes sense even beyond zero radius. In other words it seems that manifolds with zero size are non-singular as target spaces for string theory (even when they are not conformal). The cases of $CP^1$ and $CP^2$ are discussed in more detail.

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