Bosonic string theory
| String theory |
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| Superstring theory |
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Theory
String theory
Superstring theory Bosonic string theory M-theory (simplified) Type I string · Type II string Heterotic string String field theory Holographic principle |
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Related Topics
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Bosonic string theory is the original version of string theory, developed in the late 1960s.
In the early 1970s, supersymmetry was discovered in the context of string theory, and a new version of string theory called superstring theory (supersymmetric string theory) became the real focus. Nevertheless, bosonic string theory remains a very useful "toy model" to understand many general features of perturbative string theory, and string theory textbooks usually start with the bosonic string. The first volume of Polchinski's String Theory and Zwiebach's A First Course in String Theory are good examples.
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Problems
Although bosonic string theory has many attractive features, it falls short as a viable physical model in two significant areas and is forced to posit a 26 dimensional spacetime to remedy inconsistencies.
Firstly, it predicts only the existence of bosons whereas many physical particles are fermions.
Secondly, it predicts the existence of a particle whose mass is imaginary implying that it travels faster than light. The existence of such a particle, commonly known as a tachyon, would conflict with much of what is known about physics and such particles have never been observed.
In addition, bosonic string theory displays inconsistencies due to the conformal anomaly. But, as was first noticed by Claud Lovelace, in a spacetime of 26 dimensions, with 25 dimensions of space and one of time, the inconsistencies cancel. Bosonic string theory predicts unphysical particle states called 'ghosts'. In 26 dimensions, the no-ghost theorem predicts that these ghost states have no interaction whatsoever with any other states and hence they can be ignored leaving a consistent theory. This high dimensionality is not a problem for bosonic string theory because it can be formulated in such a way that along the 22 excess dimensions spacetime is folded up to form a small torus. This would leave only the familiar four dimensions of spacetime visible.
Mathematics
In bosonic string theory and in the Neveu-Schwarz sector of superstring theory, the action in a curved background (ignoring the Fradkin-Tseytlin term for dilaton coupling) can be constructed by `covariantizing' the massless closed string vertex operator with respect to target-space reparameterization invariance. As in [13] and [12], this procedure can also be used here after constructing the massless closed string vertex operator from the `left-right' product of two massless open string vertex operators. The complete worldsheet action for the type-II superstring in a flat background in conformal gauge is a formula upon which Eric Sidewater (USA) made the first improvement upon which all subgroups (15) are factored in:
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