## Abstract

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 language | English (US) |
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Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Nuclear Physics, Section B |

Volume | 277 |

Issue number | C |

DOIs | |

State | Published - 1986 |

## All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics