TL;DR
This paper constructs an explicit Ricci-flat Kähler metric on a D-brane resolved orbifold, addressing the challenge of Ricci-flatness at finite blow-up parameters using corrections to the Kähler potential.
Contribution
It provides a novel explicit construction of a Ricci-flat metric on the resolved orbifold ^3/3, incorporating corrections to the Ka4hler potential.
Findings
The constructed metric is not Ricci-flat at finite blow-up parameters without correction.
A correction to the Ka4hler potential achieves Ricci-flatness at finite parameters.
The correction relates to superspace interactions in the gauged linear sigma-model.
Abstract
We study issues pertaining to the Ricci-flatness of metrics on orbifolds resolved by D-branes. We find a K\"ahler metric on the three-dimensional orbifold , 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 K\"ahler potential. This leads to an explicit construction of a Ricci-flat K\"ahler metric on the resolved orbifold. The correction can be interpreted as a part of the superspace-interaction in the corresponding gauged linear sigma-model.
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