Superstring modifications of Einstein's equations

David J. Gross, Edward Witten

Research output: Contribution to journalArticlepeer-review

808 Scopus citations


The modifications of the classical equations of motion of the gravitational field in type II string theory are derived by studying tree-level gravitational scattering amplitudes. The effective gravitational action is determined through quartic order in the Riemann tensor. It is shown that generic Ricci-flat manifolds do not solve the modified equations, unless in addition the manifolds are Kähler (2 N-dimensional manifolds of SU(N) holonomy). Translated into sigma model language, this calculation would indicate that the N = 1 supersymmetric sigma model in 2 dimensions, with a Ricci-flat target space, is not conformally invariant, but has a nonzero beta function at four-loop order.

Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalNuclear Physics, Section B
Issue numberC
StatePublished - 1986

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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