String Theory near a Conifold Singularity

Details String Theory near a Conifold Singularity String Theory near a Conifold Singularity

1995-08-09

arxiv.org/abs/hep-th/9508044v2

Phys.Lett. B362 (1995) 73-77

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, harvmac. Some changes to manuscript and a reference added

Scientific paper

10.1016/0370-2693(95)01155-J

We demonstrate that type II string theory compactified on a singular Calabi-Yau manifold is related to $c=1$ string theory compactified at the self-dual radius. We establish this result in two ways. First we show that complex structure deformations of the conifold correspond, on the mirror manifold, to the problem of maps from two dimensional surfaces to $S^2$. Using two dimensional QCD we show that this problem is identical to $c=1$ string theory. We then give an alternative derivation of this correspondence by mapping the theory of complex structure deformations of the conifold to Chern-Simons theory on $S^3$. These results, in conjunction with similar results obtained for the compactification of the heterotic string on $K_3\times T^2$, provide strong evidence in favour of S-duality between type II strings compactified on a Calabi-Yau manifold and the heterotic string on $K_3\times T^2$.

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