§2.8: What Kind Of String Theories Are There?

There are several ways theorists can build string theories. Start with the elementary ingredient -- a tiny, wiggling string. Next, decide if it will be an open string or a closed string. Finally, choose whether the theory will have sensible quantum mechanics results or the same infinities as point theories. With these three issues in mind, here we go:

String theories are classified according to whether or not the strings are required to be closed loops, and whether or not the particle spectrum includes fermions (particles that make up matter). In order to include fermions in string theory, there must be a special kind of symmetry called supersymmetry. This pairs every boson (particle that transmits a force) with a corresponding fermion (particle that makes up matter). So supersymmetry relates the particles that transmit forces to the particles that make up matter. Without supersymmetry, we get bosonic string theory. (Remember that in string theory a particle is an excitation mode, like a note played on the string.)

No pair of known particles are supersymmetry partners of one another, so supersymmetry requires the existence of a new elementary particle for every known one. As often happens, the names are somewhat whimsical. The partners of quarks are called "squarks", the partners of electrons are called "selectrons", the partners of gluons (that carry the strong nuclear force) are called "gluinos" and so forth.

It is believed that the reason these particles have not yet been observed is because supersymmetry is a broken symmetry. As a result, the superpartners are heavier than the known elementary particles. Experiments carried out so far have not had particle beams of sufficient energy and intensity to produce them in observable numbers. Evidence for supersymmetry at high energy would be compelling evidence that string theory was a good mathematical model for the universe at the smallest distance scales. A supersymmetric string theory is called a superstring theory (hence the name "superstrings"). There are five kinds of superstring theories, shown in the table on the next page.

The final question for making a string theory is: "Can I do quantum mechanics sensibly?" (If we don't require this, we might as well just stick to the point-particle approach.) For bosonic strings, this question is only answered in the affirmative with 26 space-time dimensions. For superstrings we can whittle it down to 10. How we get down to the four space-time dimensions we observe in our world is another story.


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