Superstring Theory - Number of Superstring Theories

Number of Superstring Theories

Theoretical physicists were troubled by the existence of five separate string theories. A possible solution for this dilemma was suggested at the beginning of what is called the second superstring revolution in the 1990s, which suggests that the five string theories might be different limits of a single underlying theory, called M-theory. Unfortunately, however, to this date this remains a conjecture.

String theories
Type Spacetime dimensions SUSY generators chiral open strings heterotic compactification gauge group tachyon
Bosonic (closed) 26 N = 0 no no no none yes
Bosonic (open) 26 N = 0 no yes no U(1) yes
I 10 N = (1,0) yes yes no SO(32) no
IIA 10 N = (1,1) no no no U(1) no
IIB 10 N = (2,0) yes no no none no
HO 10 N = (1,0) yes no yes SO(32) no
HE 10 N = (1,0) yes no yes E8 × E8 no
M-theory 11 N = 1 no no no none no

The five consistent superstring theories are:

  • The type I string has one supersymmetry in the ten-dimensional sense (16 supercharges). This theory is special in the sense that it is based on unoriented open and closed strings, while the rest are based on oriented closed strings.
  • The type II string theories have two supersymmetries in the ten-dimensional sense (32 supercharges). There are actually two kinds of type II strings called type IIA and type IIB. They differ mainly in the fact that the IIA theory is non-chiral (parity conserving) while the IIB theory is chiral (parity violating).
  • The heterotic string theories are based on a peculiar hybrid of a type I superstring and a bosonic string. There are two kinds of heterotic strings differing in their ten-dimensional gauge groups: the heterotic E8×E8 string and the heterotic SO(32) string. (The name heterotic SO(32) is slightly inaccurate since among the SO(32) Lie groups, string theory singles out a quotient Spin(32)/Z2 that is not equivalent to SO(32).)

Chiral gauge theories can be inconsistent due to anomalies. This happens when certain one-loop Feynman diagrams cause a quantum mechanical breakdown of the gauge symmetry. The anomalies were canceled out via the Green–Schwarz mechanism.

Even though there are only five superstring theories, in order to make detailed predictions for real experiments information is needed about exactly what physical configuration the theory is in. This considerably complicates efforts to test string theory because there is an astronomically high number – 10500 or more – of configurations that meet some of the basic requirements to be consistent with our world. Along with the extreme remoteness of the Planck scale, this is the other major reason it is hard to test superstring theory.

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