The Freckled Instantons

TL;DR

This paper investigates instanton effects on renormalization group flows in 2D sigma models and 4D gauge theories, introducing the concept of 'freckled instantons' to unify these cases and clarify superpotential issues.

Contribution

It introduces the notion of 'freckled instantons' to unify instanton corrections in 2D and 4D theories and clarifies the nature of superpotentials and target space disconnectness.

Findings

Unified description of instanton effects in 2D and 4D theories.

Clarified the nature of superpotentials in these models.

Discovered the disconnectness of the effective target space.

Abstract

We study instanton-corrected renormalization group flow in the two dimensional sigma models and four dimensional gauge theory. In two dimensions we do that by replacing the non-linear supersymmetric ${\IC\IP}^{N-1}$ model by the gauged linear sigma model which is in the same universality class. We compare the moduli spaces of the instantons in the non-linear model and that of BPS field configurations in the linear model. We reduce the problem of matching of the parameters of the two systems to the intersection theory on the compact moduli space of the latter model. Both cases (2d and 4d) are unified by the notion of the {\it freckled instantons}. We also put an end to the discussion of the nature of the superpotentials $W \sim {\s} {\rm log} {\s}$ in 2d and 4d and discover the surprising disconnectnessness of the effective target space.