A Ricci-flat metric on D-brane orbifolds
arXiv:hep-th/9803192 · doi:10.1016/S0370-2693(98)00722-9
Abstract
We study issues pertaining to the Ricci-flatness of metrics on orbifolds resolved by D-branes. We find a Kähler metric on the three-dimensional orbifold $\C^3/\Z_3$, resolved by D-branes, following an approach due to Guillemin. This metric is not Ricci-flat for any finite value of the blow-up parameter. Conditions for the envisaged Ricci-flat metric for finite values of the blow-up parameter are formulated in terms of a correction to the Kähler potential. This leads to an explicit construction of a Ricci-flat Kähler metric on the resolved orbifold. The correction can be interpreted as a part of the superspace-interaction in the corresponding gauged linear sigma-model.
12 pages, latex. Uses amsmath and amssymb. A major typo in eq(61) corrected. The current version supersedes the journal version, which contains the typo too