English

A Ricci-flat metric on D-brane orbifolds

High Energy Physics - Theory 2023-08-30 v2

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 \C3/Z3\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 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.

Cite

@article{arxiv.hep-th/9803192,
  title  = {A Ricci-flat metric on D-brane orbifolds},
  author = {Koushik Ray},
  journal= {arXiv preprint arXiv:hep-th/9803192},
  year   = {2023}
}

Comments

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

R2 v1 2026-07-22T16:09:45.745Z