1996/04/30 by Edward Witten · 646 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Compactification (mathematics) #Cosmology and Gravitation Theories #F-theory #Heterotic string theory #Instanton #Mathematical physics #Mathematics #Moduli space #Particle physics theoretical and experimental studies #Physics #Pure mathematics #String (physics) #Superpotential #Supersymmetry #Theoretical physics #hep-th
paper · pdf · doi:10.1016/0550-3213(96)00283-0
published in Nuclear Physics B 474(2), 343-360 (Elsevier BV) · Improved explanation of selection rule, and other more minor corrections, 22 pages
arxiv created 1996/05/07 · openalex publication_date 1996/08/01 · arxiv updated 2010/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The non-perturbative superpotential can be effectively calculated in M-theory compactification to three dimensions on a Calabi-Yau four-fold X. For certain X, the superpotential is identically zero, while for other X, a non-perturbative superpotential is generated. Using F-theory, these results carry over to certain Type IIB and heterotic string compactifications to four dimensions with N=1 supersymmetry. In the heterotic string case, the non-perturbative superpotential can be interpreted as coming from space-time and world-sheet instantons; in many simple cases contributions come only from finitely many values of the instanton numbers.