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Abstract
We study the nonperturbative superpotential in E_{8} × E_{8} heterotic string theory on a nonsimply connected CalabiYau manifold X, as well as on its simply connected covering space X˜. The superpotential is induced by the string wrapping holomorphic, isolated, genus 0 curves. According to the residue theorem of Beasley and Witten, the nonperturbative superpotential must vanish in a large class of heterotic vacua because the contributions from curves in the same homology class cancel each other. We point out, however, that in certain cases the curves treated in the residue theorem as lying in the same homology class, can actually have different area with respect to the physical Kahler form and can be in different homology classes. In these cases, the residue theorem is not directly applicable and the structure of the superpotential is more subtle. We show, in a specific example, that the superpotential is nonzero both on X˜ and on X. On the nonsimply connected manifold X, we explicitly compute the leading contribution to the superpotential from all holomorphic, isolated, genus 0 curves with minimal area. The reason for the nonvanishing of the superpotental on X is that the second homology class contains a finite part called discrete torsion. As a result, the curves with the same area are distributed among different torsion classes and, hence, do not cancel each other.
Original language  English 

Article number  38 
Journal  Journal of High Energy Physics 
Volume  2017 
Issue number  1 
DOIs  
Publication status  Published  10 Jan 2017 
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 2 Finished

Novel Conformal Techniques in Quantum Field Theory, Gravity and Supergravity
Kuzenko, S., Buchbinder, E., TartaglinoMazzucchelli, G., Theisen, S. & Tseytlin, A.
ARC Australian Research Council
1/01/14 → 30/06/17
Project: Research

Relating string theory and particle physics: model building and strong coupling phenomena
ARC Australian Research Council
1/01/12 → 30/06/17
Project: Research