Editing Non-linear sigma model (section)

==Renormalization==
This model proved to be relevant in string theory where the two-dimensional manifold is named '''[[worldsheet]]'''. Appreciation of its generalized renormalizability was provided by [[Daniel Friedan]].<ref name="Frie80">
{{cite journal|last=Friedan|first=D.|author-link=Daniel Friedan|title=Nonlinear models in 2+ε dimensions | journal =  Physical Review Letters| volume = 45 | issue = 13| pages = 1057–1060 | year = 1980 |doi= 10.1103/PhysRevLett.45.1057 | bibcode=1980PhRvL..45.1057F|url=https://digital.library.unt.edu/ark:/67531/metadc841801/}}</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>
{{math|''R<sub>ab</sub>''}} being the [[Ricci tensor]] of the target manifold.

This represents a [[Ricci flow]], obeying [[Einstein field equations]] for the target manifold as a fixed point. The existence of such a fixed point is relevant, as it grants, at this order of perturbation theory, that [[conformal field theory|conformal invariance]] is not lost due to quantum corrections, so that the [[quantum field theory]] of this model is sensible (renormalizable). 

Further adding nonlinear interactions representing flavor-chiral anomalies results in the [[Wess–Zumino–Witten model]],<ref>{{cite journal |first=E. |last=Witten |s2cid=122018499 |title=Non-abelian bosonization in two dimensions |journal=[[Communications in Mathematical Physics]] |volume= 92| issue= 4 |year=1984 | pages= 455–472 | doi= 10.1007/BF01215276|bibcode = 1984CMaPh..92..455W |url=http://projecteuclid.org/euclid.cmp/1103940923 }}</ref>  which 
augments the geometry of the flow to include [[Torsion tensor|torsion]], preserving renormalizability and leading to an [[infrared fixed point]] as well, on account of [[teleparallelism]] ("geometrostasis").<ref>{{Cite journal | last1 = Braaten | first1 = E. | last2 = Curtright | first2 = T. L. | last3 = Zachos | first3 = C. K. | doi = 10.1016/0550-3213(85)90053-7 | title = Torsion and geometrostasis in nonlinear sigma models | journal = Nuclear Physics B | volume = 260 | issue = 3–4 | pages = 630 | year = 1985 |bibcode = 1985NuPhB.260..630B }}</ref>
{{further|Ricci flow}}