Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-04-30
JHEP 9906 (1999) 021
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, LaTeX, no figures; v2: discussion of FI-couplings in section 3 and appendix enlarged, version to appear in JHEP
Scientific paper
10.1088/1126-6708/1999/06/021
We discuss how to obtain an N=(2,2) supersymmetric SU(3) gauge theory in two dimensions via geometric engineering from a Calabi-Yau 4-fold and compute its non-perturbative twisted chiral potential. The relevant compact part of the 4-fold geometry consists of two intersecting P^1's fibered over P^2. The rigid limit of the local mirror of this geometry is a complex surface that generalizes the Seiberg-Witten curve and on which there exist two holomorphic 2-forms. These stem from the same meromorphic 2-form as derivatives w.r.t. the two moduli, respectively. The middle periods of this meromorphic form give directly the twisted chiral potential. The explicit computation of these and of the four-point Yukawa couplings allows for a non-trivial test of the analogue of rigid special geometry for a 4-fold with several moduli.
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