A Ricci-flat metric on D-brane orbifolds

Details A Ricci-flat metric on D-brane orbifolds A Ricci-flat metric on D-brane orbifolds

1998-03-23

arxiv.org/abs/hep-th/9803192v1

Phys.Lett. B433 (1998) 307-317

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, latex. Uses amsmath and amssymb

Scientific paper

10.1016/S0370-2693(98)00722-9

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 $\C^3/\Z_3$, 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.

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