String theory became a hot subject in the mid-1980s when it became clear that it might
give a deeper understanding of the origins of the standard model and a consistent quantum
theory containing gravity. At that time five consistent string theories were known,
each of which requires ten spacetime dimensions and supersymmetry. They are called:
Type I, Type IIA, Type IIB
SO(32) heterotic, E8 × E8 heterotic
Each of these theories is entirely free of adjustable dimensionless parameters. All dimensionless
parameters arise in either of two possible ways:
• dynamically as the expectation values of scalar fields
• as integers that count something such as topological invariants, physical objects (branes),
or quantized fluxes.
One scheme looked particularly promising in the mid-1980s. Specifically, the E8 × E8 heterotic
theory has consistent vacuum solutions in which six spatial dimensions form a compact
Calabi–Yau manifold, which has SU(3) holonomy, and the other four dimensions form
Minkowski spacetime [4]. Thus, the ten-dimensional spacetime M10 is a direct product
M10 = CY6 × M3,1.
The effective four-dimensional theories that characterize such solutions at low energies
have the following attractive features:
• They have the structure of supersymmetric grand unified theories. The well-known
advantages of low-energy supersymmetry and grand unification are therefore naturally
incorporated.
• Each solution has a definite number of families of quarks and leptons determined by
the topology of the CY space.
• The standard model gauge symmetry is embedded in one E8 factor, and there is a
hidden sector, associated to the second E8 factor. Supersymmetry can break dynamically
(by gluino condensation) in the hidden sector. This breaking is communicated
gravitationally to the visible sector. Such schemes suppress unwanted flavor-changing
neutral currents, though possibly not as much as is required.
• There are several good dark-matter candidates: The lightest supersymmetric particle,
called the LSP (perhaps a neutralino) is absolutely stable if there is an unbroken R
symmetry, as generally supposed to be the case. A stable neutralino has the right properties
for weakly interacting cold dark matter (a WIMP). Other possibilities include
gravitinos, axions, and hidden-sector particles.
Despite the exuberance that was in the air in 1985,1
there was much that was not yet
understood. The successes were qualitative, and there were many problems and puzzling
questions. Some of these problems and questions were the following:
• Hundreds of Calabi–Yau manifolds were known (now there are many thousands).
Which one of them, if any, is the right one? Is there a principle (other than agreement
with observations) by which the right one can be determined? Are there string-theory
based schemes other than CY compactification of the E8 × E8 heterotic theory that
can give quasi-realistic solutions?
• Why are there four other consistent superstring theories? After all, we only need
one fundamental theory. Are some of them inconsistent, or else, could some of them
somehow be equivalent?
• The CY compactification scenario was analyzed using perturbation theory, but there
is no good reason to believe that the string coupling should be small. What new
nonperturbative features appear at strong coupling? Does the same qualitative picture
continue to hold at strong coupling?
• The CY solutions typically give many massless scalars (called moduli). Since the moduli
have gravitational strength interactions, they are ruled out by standard tests of GR.
How can we get rid of them? The effective potential does not depend on the values of
the moduli, so they describe flat directions. One should somehow stabilize the moduli
by generating an effective potential with isolated minima and no flat directions.
• What ensures that the vacuum energy density (or dark energy) is sufficiently small,
namely of order 10−120 in Planck units? In 1985 it was generally believed to be zero,
so one popular idea was to look for a symmetry principle that would enforce this. It is
just as well that such a symmetry was never found, since we now know that the vacuum
energy density is not exactly zero. A generic nonsupersymmetric vacuum is expected
