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Joshua Davis (talk | contribs) Added a litle bit about central charges and critical dimension |
Joshua Davis (talk | contribs) mentioned relation of dilaton and string coupling with link to coupling constant |
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In order for a [[string theory]] to be consistent, the [[worldsheet]] theory must be conformally invariant. The obstruction to [[conformal symmetry]] is known as the [[Weyl anomaly]] and is proportional to the [[central charge]] of the worldsheet theory. In order to preserve conformal symmetry the Weyl anomaly, and thus the central charge, must vanish. For the [[bosonic string]] this can be accomplished by a worldsheet theory consisting of 26 free [[bosons]]. Since each boson is interpreted as a flat spacetime dimension, the critical dimension of the bosonic string is 26. A similar logic for the [[superstring]] results in 10 free bosons(and 10 free [[fermions]] as required by worldsheet [[supersymmetry]]). The bosons are again intepreted as spacetime dimensions and so the critical dimension for the superstring is 10.
The non-critical string is not formulated with the critical dimension, but nonetheless has vanishing Weyl anomaly. A worldsheet theory with the correct central cahrge can be constructed by introducing a non-trivial target space, commonly by giving a spatially varying [[expectation value]] to the [[dilaton]]. Since the dilaton is related to the string [[coupling constant]], this leads to a region where the coupling is weak(and so perturbation theory is valid) and another region where the theory is strongly coupled.
== Two-dimensional String Theory ==
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