On the Four-Dimensional Effective Action of Strongly Coupled Heterotic String Theory

The low-energy D = 4, N = 1 effective action of the strongly coupled heterotic string is explicitly computed by compactifying Hořava-Witten theory on the deformed Calabi-Yau threefold solution due to Witten. It is shown that, to order κ, the Kähler potential is identical to that of the weakly coupled theory. Furthermore, the gauge kinetic functions are directly computed to order κ and shown to receive a non-vanishing correction. We find the full threshold correction is exactly twice that originally calculated by Witten. Also, we compute gauge matter terms in the Kähler potential to the order κ and find a nontrivial correction to the dilaton term. Part of those corrections arise from background fields that depend on the orbifold coordinate and are excited by four-dimensional gauge field source terms. Supported by Deutsche Forschungsgemeinschaft (DFG) and Nato Collaborative Research Grant CRG. 940784. Supported in part by a Senior Alexander von Humboldt Award