Non-linear sigma model: Difference between revisions

Revision as of 18:37, 27 August 2015

Revision as of 17:51, 28 August 2015

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:<math>\sqrt{\det g}\mathcal{D}\Sigma.</math>

==Renormalization==

This model proved to be relevant in string theory where the two-dimensional manifold is named '''worldsheet'''. ProofAppreciation of its generalized renormalizability was givenprovided by [[Daniel Friedan]].<ref name="Frie80">

{{cite journal|last=Friedan|first=D.|authorlink=Daniel Friedan|title=Nonlinear models in 2+ε dimensions | journal = PRL | volume = 45 | issue = 13| pages = 1057 |publisher=|___location=| year = 1980 | url = http://link.aps.org/doi/10.1103/PhysRevLett.45.1057 |doi= 10.1103/PhysRevLett.45.1057 | bibcode=1980PhRvL..45.1057F}}</ref> He showed that the theory admits a renormalization group equation, at the leading order of perturbation theory, in the form

:<math>\lambda\frac{\partial g_{ab}}{\partial\lambda}=\beta_{ab}(T^{-1}g)=R_{ab}+O(T^2)~,</math>