2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105931We present the evidence for two conjectures related to the twistor string. The first conjecture states that two super-Calabi Yaus -- the supertwistor space and the superambitwistor space -- form a mirror pair. The second conjecture is that the B-model on the twistor space can be seen as describing a 4-dimensional gravitational theory, whose partition function should involve a sum over ''space-time foams'' related to D1 branes in the topological string.9 pages, 1 fig. Contribution to the proceedings of the Workshop ``Supersymmetries and Quantum Symmetries'', 27-31 July 2005, JINR, Dubna, RussiaHigh Energy Physics - Theorytext