Non-critical string theory: Difference between revisions

Revision as of 05:46, 28 September 2006

Revision as of 05:54, 28 September 2006

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== The Critical Dimension and Central Charge ==

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 symmetryconformalsymmetry 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 charge can be constructed by introducing a non-trivial target space, commonly by giving an [[expectation value]] to the [[dilaton]] which varies linearly along some spacetime direction. For this reason non-critical string theory is sometimes called the linear dilaton theory. Since the dilaton is related to the string [[coupling constant]], this theory contains a region where the coupling is weak(and so perturbation theory is valid) and another region where the theory is strongly coupled.

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** Vol. 1: An introduction to the bosonic string. ISBN 0-521-63303-6.

** Vol. 2: Superstring theory and beyond. ISBN 0-521-63304-4.

== See also ==

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* [[Weyl anomaly]]

* [[Central charge]]

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