CHAPTER 10
Attempt at a Synthesis
What is the use of string theories? What is their connection with the
physical problems described in the other chapters? There is no final
answer to these questions. In this chapter I shall describe reasons to
believe that string theories are important and perhaps present the
master-key to the most fundamental problems.
Three kinds of questions will be in the centre of our attention. We
begin with the project of grand unification on the string basis, then
describe the 3-D Ising model and conclude with 4-D chromodynamics.
10.1 Long Wave Oscillations of Strings in Critical Dimensions
We have seen in the previous chapter that string theories in critical
dimension contain massless spin 2 particles in their spectrum (and their
superpartners for superstrings). Since the only consistent interaction for
these particles is the gravitational one, these string theories must
contain within themselves a theory of gravity. While in the low energy
limit this theory will necessarily be Einstein-like, for high energies it will
have good regular behaviour because strings are extended objects.
The basic idea of unified theories is to presume that all our lowenergy world arises from massless string excitations which include
super-gravitons, gauge fields and matter fields. All massive modes of
strings are presumed to be very heavy (of the order of the Planck mass),
and therefore unobservable.
Let us explain how this idea can be implemented.
First of all, why and when do we have massless excitations in the
string theory? To find the partial answer to this question, let us recall
that an ordinary string has the action
S =
d^x d^x
( 10.1)
253
DOI: 10.1201/9780203755082-10
Attempt at a Synthesis
What is the use of string theories? What is their connection with the
physical problems described in the other chapters? There is no final
answer to these questions. In this chapter I shall describe reasons to
believe that string theories are important and perhaps present the
master-key to the most fundamental problems.
Three kinds of questions will be in the centre of our attention. We
begin with the project of grand unification on the string basis, then
describe the 3-D Ising model and conclude with 4-D chromodynamics.
10.1 Long Wave Oscillations of Strings in Critical Dimensions
We have seen in the previous chapter that string theories in critical
dimension contain massless spin 2 particles in their spectrum (and their
superpartners for superstrings). Since the only consistent interaction for
these particles is the gravitational one, these string theories must
contain within themselves a theory of gravity. While in the low energy
limit this theory will necessarily be Einstein-like, for high energies it will
have good regular behaviour because strings are extended objects.
The basic idea of unified theories is to presume that all our lowenergy world arises from massless string excitations which include
super-gravitons, gauge fields and matter fields. All massive modes of
strings are presumed to be very heavy (of the order of the Planck mass),
and therefore unobservable.
Let us explain how this idea can be implemented.
First of all, why and when do we have massless excitations in the
string theory? To find the partial answer to this question, let us recall
that an ordinary string has the action
S =
d^x d^x
( 10.1)
253
DOI: 10.1201/9780203755082-10