String Theory Demystified

188 String Theory Demystifi ed
superstring theories, and we also saw that it is possible to construct a theory
consisting only of bosons. Actually you can list four different bosonic string
theories, which we will do here.
BOSONIC STRING THEORY
We began our look at strings by considering bosonic string theory. This is an
unrealistic theory because we know that the real world contains particles that are
fermions. Nonetheless bosonic string theory provides an easier framework that can
be used to illustrate the key ideas and techniques of string theory.
Some key aspects of bosonic string theory you should remember are
• It introduces the concept of extra spatial dimensions. In order to avoid
ghosts (states with negative norm) we were forced to accept that there are
26 space-time dimensions.
• The ground state (the lowest energy or lowest excitation mode of the string)
has a negative mass-squared ( m / ).
2
=− 1 α ′ This state is called a tachyon.
The presence of a tachyon in the theory indicates that the ground state
or vacuum is unstable. Note that in relativity, tachyons are particles that
travel faster than the speed of light. Therefore the tachyon is a physically
unrealistic particle. There is no known way to remove tachyon states from
bosonic string theory.
• Bosonic string theory always includes gravity. This is indicated by the
presence of a spin-2 state called the graviton. This is a hint that string theories
provide a framework for the unifi cation of all known physical interactions.
• Bosonic string theories also include a state called the dilaton. This is a
scalar fi eld which is denoted byϕ . It is related to the coupling constant g
via g = exp ϕ , where ϕ is the vacuum expectation value of the dilaton
fi eld. If you need to brush up on your quantum fi eld theory, note that the
coupling constant determines the strength of an interaction. The dilaton
fi eld is dynamical (it is space-time dependent), so in string theory we obtain
a dramatic result that the string coupling constant can be dynamical. The
dilaton is also known as the gravitational scalar fi eld and may play a role
in the recently discovered nonzero cosmological constant.
Strings can be either open or closed and can be oriented or unoriented. If a string
is oriented, this means that directions along the string are unequivalent. So you can
tell which way you’re going along the string. By choosing open or closed strings
and oriented or unoriented strings, we can actually construct four different bosonic
string theories.