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arXiv · hep-th/9709146

Fayet-Iliopoulos Potentials from Four-Folds

Wolfgang Lerche
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Abstract

We show how certain non-perturbative superpotentials W, which are the two-dimensional analogs of the Seiberg-Witten prepotential in 4d, can be computed via geometric engineering from 4-folds. We analyze an explicit example for which the relevant compact geometry of the 4-fold is given by $P^1$ fibered over $P^2$. In the field theory limit, this gives an effective U(1) gauge theory with N=(2,2) supersymmetry in two dimensions. We find that the analog of the SW curve is a K3 surface, and that the complex FI coupling is given by the modular parameter of this surface. The FI potential itself coincides with the middle period of a meromorphic differential. However, it only shows up in the effective action if a certain 4-flux is switched on, and then supersymmetry appears to be non-perturbatively broken. This can be avoided by tuning the bare FI coupling by hand, in which case the supersymmetric minimum naturally corresponds to a singular K3.

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Wolfgang Lerche. 1997-09-19. Fayet-Iliopoulos Potentials from Four-Folds. https://doi.org/10.1088/1126-6708%2F1997%2F11%2F004

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