Re: What's the difference between the different string theories?

Dear Spencer,

Great question!  I could write hundreds of pages in response, but I
will not.  Instead, because others have already written hundreds of
pages on this topic, I will give you an extremely condensed answer and
point you to further elaborations and background material.

When we try to describe the matter and forces of Nature in terms of
zero-dimensional point particles, the calculations give nonsensical
results.  One way around this problem is to describe the fundamental
objects of Nature as extremely tiny one-dimensional strings.  The
physical properties of the object (mass, spin, etc.) are associated
with the way that the string vibrates.

There are five (and only five) types of superstring theory which are
free of mathematical inconsistencies.  The adjective "super" means
that the string theory entails both fermions (matter, like quarks and
electrons) and bosons (force carriers, such as the photon and gluon),
and is thus capable of describing everything in the Universe.

Type I - the first to be discovered, this is the only superstring
theory which contains both open and closed strings (think of broken
and unbroken rubber bands) which can link up with one another or break
apart.  All the other types deal exclusively with closed strings.  The
open strings can carry charges, labels which identify the particle, on
their free ends.

Type IIA and Type IIB - the first is "non-chiral" and the second is
"chiral".  Non-chiral means that a certain particle in the theory can
spin along its direction of motion or opposite to its direction of
motion.  In the chiral theory, this particle can only spin one way.
Another word for chirality is "handedness".  For example, most screws
are right-handed because they advance when rotated clockwise.  If all
the screws in your theory were right-handed, then your theory would be
chiral.  If your theory contains both right- and left-handed screws,
then your theory is non-chiral.  Of the five superstring theories,
only Type IIA is non-chiral.

Type II theories have two "supersymmetries", while the other three
theories have only one supersymmetry.  Briefly, a supersymmetry is a
relation between fermions and bosons.

SO(32) Heterotic and E8 x E8 Heterotic - "heterotic" means that
vibrations propagating around the closed string in one direction are
distinct from vibrations propagating around in the opposite direction;
that is, they correspond to completely different particles.

The first is based on a symmetry called SO(32), which is the
32-dimensional analog of rotations.  For example, a two-dimensional
circular disk can be rotated in the plane and still appears the same
-- it has symmetry SO(2), for rotations in two dimensions.  A sphere
in three dimensions has rotational symmetry SO(3).

The second is based on two copies of the E8 symmetry.  This theory
describes two parallel universes which can only interact with each
other through the gravitational force.  We inhabit one copy; the other
copy is referred to as the "shadow" universe.  A shadow planet could
in theory exist very close to Earth, but we would not be able to see
it because its shadow photons would not interact with our eyes.  In
fact, shadow matter could pass right through ordinary matter because
the shadow quarks and shadow electrons do not "feel" ordinary quarks
and electrons.  We could, however, feel the shadow planet's gravity.

These five superstring theories and eleven dimensional supergravity
(which is not a string theory) are related by duality transformations.
That is, one theory in a certain limit looks like another theory in a
different limit.  Because it is possible to transform any of these six
theories into any other, they all appear to be limiting cases of one
all-encompassing theory dubbed "M-theory".



References:

The Search for Superstrings, Symmetry, and the Theory of Everything
by John Gribbin, ISBN 0-316-32614-3.
 http://www.superstringtheory.com
 http://www.physics.ucsb.edu/~jpierre/strings/

Try your own web search for "string theory" and/or "M-theory".

--Randall J. Scalise    http://www.phys.psu.edu/~scalise/