Bosonic string theory
is the original version of string theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
, developed in the late 1960s
The 1960s was the decade that started on January 1, 1960, and ended on December 31, 1969. It was the seventh decade of the 20th century.The 1960s term also refers to an era more often called The Sixties, denoting the complex of inter-related cultural and political trends across the globe...
In the early 1970s, supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
was discovered in the context of string theory, and a new version of string theory called superstring theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings...
(supersymmetric string theory) became the real focus. Nevertheless, bosonic string theory remains a very useful "toy model
In physics, a toy model is a simplified set of objects and equations relating them that can nevertheless be used to understand a mechanism that is also useful in the full, non-simplified theory....
" to understand many general features of perturbative string theory, and string theory textbooks usually start with the bosonic string. The first volume of Polchinski
Joseph Polchinski is a physicist working on string theory. He graduated from Canyon del Oro High School in Tucson, Arizona in 1971, obtained his B.S. degree from Caltech in 1975, and his Ph.D. from the University of California, Berkeley in 1980 under the supervision of Stanley Mandelstam...
's String Theory
and Zwiebach's A First Course in String Theory
are good examples.
Although bosonic string theory has many attractive features, it falls short as a viable physical model
A physical model is a smaller or larger physical copy of an object...
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
An imaginary number is any number whose square is a real number less than zero. When any real number is squared, the result is never negative, but the square of an imaginary number is always negative...
implying that it travels faster than light
Faster-than-light communications and travel refer to the propagation of information or matter faster than the speed of light....
. The existence of such a particle, commonly known as a tachyon
A tachyon is a hypothetical subatomic particle that always moves faster than light. In the language of special relativity, a tachyon would be a particle with space-like four-momentum and imaginary proper time. A tachyon would be constrained to the space-like portion of the energy-momentum graph...
, 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
Conformal anomaly is an anomaly i.e. a quantum phenomenon that breaks the conformal symmetry of the classical theory.A classically conformal theory is a theory which, when placed on a surface with arbitrary background metric, has an action that is invariant under rescalings of the background metric...
. 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
In geometry, a torus is a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle...
. This would leave only the familiar four dimensions of spacetime visible.
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  and ,
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: