TY - JOUR

T1 - Superstring modifications of Einstein's equations

AU - Gross, David J.

AU - Witten, Edward

N1 - Funding Information:
in part by NSF Grant PHY80-19754.

PY - 1986

Y1 - 1986

N2 - 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.

AB - 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.

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U2 - 10.1016/0550-3213(86)90429-3

DO - 10.1016/0550-3213(86)90429-3

M3 - Article

AN - SCOPUS:0002679653

SN - 0550-3213

VL - 277

SP - 1

EP - 10

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - C

ER -