SUPERSTRINGS! Supersymmetric Strings 

There are two types of particles in nature - fermions and bosons. A fundamental theory of nature must contain both of these types. When we include fermions in the worldsheet theory of the string, we automatically get a new type of symmetry called supersymmetry which relates bosons and fermions. Fermions and bosons are grouped together into supermultiplets which are related under the symmetry. This is the reason for the "super" in "superstrings".

A consistent quantum field theory of superstrings exists only in 10 spacetime dimensions! Otherwise there are quantum effects which render the theory inconsistent or 'anomalous'. In 10 spacetime dimensions the effects can precisely cancel leaving the theory anomaly free. It may seem to be a problem to have 10 spacetime dimensions instead of the 4 spacetime dimensions that we observe, but we will see that in getting from 10 to 4 we actually find some interesting physics.

In terms of weak coupling perturbation theory there appear to be only five different consistent superstring theories known as Type I SO(32), Type IIA, Type IIB, SO(32) Heterotic and E8 x E8 Heterotic.
 

Type IIB Type IIA E8 x E8 Heterotic SO(32) Heterotic Type I SO(32)
String Type Closed Closed Closed Closed Open 
(& closed)
10d Supersymmetry N=2 
(chiral)
N=2 
(non-chiral)
N=1 N=1 N=1
10d Gauge groups none none E8 x E8 SO(32) SO(32)
D-branes -1,1,3,5,7 0,2,4,6,8 none none 1,5,9
  We see that the Heterotic theories don't contain D-branes. They do however contain a fivebrane soliton which is not a D-brane. The IIA and IIB theories also contain this fivebrane soliton in addition to the D-branes. This fivebrane is usually called the "Neveu-Schwarz fivebrane" or "NS fivebrane".

It is worthwhile to note that the E8 x E8 Heterotic string has historically been considered to be the most promising string theory for describing the physics beyond the Standard Model.  It was discovered in 1987 by Gross, Harvey, Martinec, and Rohm and for a long time it was thought to be the only string theory relevant for describing our universe.  This is because the SU(3) x SU(2) x U(1) gauge group of the standard model can fit quite nicely within one of the E8 gauge groups.  The matter under the other E8 would not interact except through gravity, and might provide a answer to the Dark Matter problem in astrophysics.  Due to our lack of a full understanding of string theory, answers to questions such as how is supersymmetry broken and why are there only 3 generations of particles in the Standard Model have remained unanswered.  Most of these questions are related to the issue of compactification (discussed on the next page).  What we have learned is that string theory contains all the essential elements to be a successful unified theory of particle interactions, and it is virtually the only candidate which does so.  However, we don't yet know how these elements specifically come together to describe the physics that we currently observe.


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