General form of string corrections to supersymmetry transformation in D=10, N=1 supergravity (original) (raw)

We present the O(a' 3) heterotic string corrections to the supersymmetry transformation rules of D= 10, N= I supergravity multiplet, which satisfy the on-shell closure of supersymmetry. We also generalize this result to higher orders in a', assuming a natural form of the leading O (o~'") heterotic string corrections to the effective action of the supergravity multiplet. We find no modification to the Killing spinor equations for the gravitino and dilatino at O(a' 5) or higher, whenever fermionic condensates are absent. 1. Introduction. One of the most important features of ten-dimensional string theories [ 1 ] is the possibility of non-trivial (chiral) compactification into four-dimensional space-time (D=4) in the point field theory limit. In particular, in the heterotic string theory with the gauge group Es × E8 [2], the compactification on Calabi-Yau manifolds with SU(3) holonomy gives rise to D= 4, N= 1 surviving supersymmetry with the grand unification group E 6 [31. The analysis in ref. [ 3 ] was based on the tree-level O(c~') correction to the D= 10, N= 1 supergravity, that arise from the Green-Schwarz anomaly cancellation mechanism [4]. Recently, higher order corrections have been obtained by tree-level string amplitude calculations in D= 10 [5,6], and by amodel fl-function calculations in D = 2 [ 7 ]. Essential agreement between these two kinds of calculations has been found up to O(a'4). It is also claimed that the Calabi-Yau manifold is the solution of the treelevel field equations in D = 10 to all orders in ce' [ 8 ]. The original motivation [3] of considering the Calabi-Yau manifold for surviving supersymmetry, however, has become obscure, because the covariant supersymmetry transformation rules in D = 10 with higher order corrections in or' needed for Killing spi