Tensoring Heterotic Superstring Theories

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The left-moving and right-moving modes of a string can be separated and treated as different theories. In 1984 it was realized that consistent string theories could be built by combining a bosonic string theory moving in one direction along the string, with a supersymmetric string theory with a single q1 moving in the opposite direction. These theories are called heterotic superstring theories. That sounds crazy — because bosonic strings live in 26 dimensions but supersymmetric string theories live in 10 dimensions. But the extra 16 dimensions of the bosonic side of the theory aren’t really spacetime dimensions. Heterotic string theories are supersymmetric string theories living in ten spacetime dimensions. Heterotic string theories are built by tensoring a left- and a right-  moving string which do not have the same base fields. More explicitly, it is constructed by tensoring the right-moving super string with 10 left-moving bosonic and 32 internal left-moving fermionic fields. Internal here means that the field does not transform under Lorentz-transformations, this implies that the boundary conditions on these allow for rotations. The two types of heterotic theories that are possible come from the two types of gauge symmetry that give rise to quantum mechanically consistent theories. The first is SO(32) and the second is the more exotic combination called E8XE8. The E8XE8 heterotic theory was previously regarded as the only string theory that could give realistic physics, until the mid-1990s, when additional possibilities based on the other theories were identified.

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One thought on “Tensoring Heterotic Superstring Theories

  1. […] Superstrings provided a perturbatively finite theory of gravity which, after compactification down to 3+1 dimensions, seemed potentially capable of explaining the strong, weak and electromagnetic forces of the Standard Model, including the required chiral representations of quarks and leptons. However, there appeared to be not one but five seemingly different but mathematically consistent superstring theories: the E8 × E8 heterotic string, the SO(32) heterotic string, the SO(32) Type I string, and Types IIA and IIB strings. Each of these theories corresponded to a different way in which fermionic degrees of freedom could be added to the string worldsheet. […]

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