String theory for particles is equivalent to quantum chromodynamics for fields {duality hypothesis}.
String theories can use different geometries to describe the same situations {geometrical duality}. A large finite dimension can behave equivalently to a small one, because a wrapped-around-dimension string can exchange with an unwrapped-in-dimension string, or because Calubi-Yau shapes can exchange number of odd-dimensional holes with number of even-dimensional holes.
Because strings have two motion modes, which can exchange, in each dimension, which can exchange, strings with small and large dimensions have same physical effects {T-duality}. Because strings have two motion modes, which can exchange, in each dimension, which can exchange, closed strings and open strings also have T-duality.
Because strings have two motion modes, which can exchange, in each dimension, which can exchange, physical systems can have either or both of two space-time geometries {mirror symmetry}.
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Date Modified: 2022.0225