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CHAPTER 10 A Summary of Superstring Theory
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If a bosonic string theory has open strings, it automatically includes closed strings as well. This is due to the dynamical behavior of strings. If a string is open, it is possible for the endpoints to join together, forming a closed string state. Let s summarize the four possibilities for bosonic string theory. If a bosonic string theory only includes closed strings that are oriented, then the spectrum of the theory includes the following states: Tachyon Massless antisymmetric tensor Dilaton Graviton Now, suppose that we only have closed strings, but the theory describes unoriented strings instead. That is, we can t tell which direction we are moving along the string. In this case, the theory no longer includes a massless vector boson. We can summarize the key aspects of the spectrum as Tachyon Dilaton Massless state which is the graviton Now let s turn to bosonic string theories that include open as well as closed strings. Again, we can choose strings that are oriented and strings that are unoriented. The oriented theory is characterized by Tachyon Dilaton Graviton A massless antisymmetric tensor The closed string and open string tachyons are distinct. Choosing oriented open + closed bosonic string theory gives us Tachyon Dilaton Massless graviton There is also a massless vector state for open strings, which can be oriented or unoriented. So we see that all bosonic string theories are plagued by the presence of a tachyon state. They have an unstable vacuum and do not include fermions. As a result, we are forced to consider superstring theories.
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String Theory Demysti ed
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Superstring Theory
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Superstring theory is a generalization of bosonic string theory which extends the theory to include fermions. There are ve different superstring theories. We use the word super in our description of them because all ve theories are based on a theory of physics known as supersymmetry. This theory is characterized by the idea that each fermion has a bosonic partner and vice versa. Some examples are given in Table 10.1. The existence of supersymmetry is a good indirect test of string theory. For string theory to be true, supersymmetry must exist in nature. At the time of writing no super-partner has ever been discovered, so supersymmetry either doesn t exist in nature or it has been broken. One way it could be broken is that the superpartners are extremely massive. This means it would take high energies to see them. The Large Hadron Collider (LHC) set to begin operation in 2008 may be powerful enough to detect supersymmetry. So, superstring theory includes supersymmetry, which allows us to introduce fermions into the theory. It also includes ghost states, which are removed in an analogous, manner to what we saw in bosonic string theory. When the ghost states are removed we arrive at the second general characteristic of superstring theory: There are 10 space-time dimensions. There are two ways to introduce supersymmetry into string theory, reviewed in Chaps. 7 and 9, respectively: The RNS formalism adds supersymmetry to the worldsheet. The GS formalism adds supersymmetry to space-time. We can still characterize superstring theories by noting whether or not they include open and/or closed strings, and whether those strings are oriented or unoriented. In addition, a superstring theory can be characterized by the number of supercharges used in the theory. This is done by saying that a theory with N = m
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Table 10.1 A listing of some particles and their postulated super-partners.
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Partner Photon (spin 1) Graviton (spin 2) Quark (spin 1/2) Electron (spin 1/2) Gluon (spin 0) Superpartner Photino (spin 1/2) Gravitino (spin 3/2) Squark (spin 0) Selectron (spin 0) Gluino (spin 1/2)
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CHAPTER 10 A Summary of Superstring Theory
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supercharges has N = m supersymmetry. Finally, we can characterize each superstring theory by the gauge symmetry that it admits. All superstring theories eliminate the tachyon from the spectrum and include a graviton, so superstring theory naturally describes gravity.
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