Constraints on low-dimensional string compactifications

S. Sethi, C. Vafa, E. Witten

Research output: Contribution to journalArticlepeer-review

317 Scopus citations


We study the restrictions imposed by cancellation of the tadpoles for two-, three-, and four-form gauge fields in string theory, M-theory and F-theory compactified to two, three and four dimensions, respectively. For a large class of supersymmetric vacua, turning on a sufficient number of strings, membranes and three-branes, respectively, can cancel the tadpoles, and preserve supersymmetry. However, there are cases where the tadpole cannot be removed in this way, either because the tadpole is fractional, or because of its sign. For M-theory and F-theory compactifications, we also explore the relation of the membranes and three-branes to the non-perturbative space-time superpotential.

Original languageEnglish (US)
Pages (from-to)213-224
Number of pages12
JournalNuclear Physics B
Issue number1-2
StatePublished - Nov 25 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • F-theory
  • M-theory
  • Strings


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