Skip to main content
SpringerLink
Log in

Renormalization group flow for general σ-models

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

The renormalization group flow for σ-models with base space of dimension 1 or 2 is investigated. In two dimensions it is shown that the flow is singular towards the UV for a generic target space. In one dimension it is shown that there are IR fixed points coming from negatively curved symmetric spaces.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Friedan, D.: Nonlinear models in 2+ℰ dimensions. Phys. Rev. Lett.45, 13, 1057 (1980); Ann. Phys.163, 2, 318 (1985)

    Google Scholar 

  2. Brézin, E., Le Guillou, J.C., Zinn-Justin, J.: Discussion of critical phenomena for generaln-vector models. Phys. Rev. B10, 3, 892 (1974)

    Google Scholar 

  3. Alvarez-Gaumé, L., Ginsparg, P.: Finiteness of Ricci-flat nonlinear σ models. Commun. Math. Phys.102, 2, 311 (1985)

    Google Scholar 

  4. Gawedzki, K., Kupiainen, A.: In preparation

  5. Gross, D.: Applications of the renormalization group. In: Methods in field theory. Balian, R., Zinn-Justin, J. (eds.). Amsterdam: North-Holland 1975

    Google Scholar 

  6. Gawedzki, K., Kupiainen, A.: Gross-Neveu model through convergent perturbation expansions. Commun. Math. Phys.102, 1 (1985)

    Google Scholar 

  7. Hamilton, R.: Three-manifolds with positive Ricci curvature. J. Differ. Geom.17, 255 (1982)

    Google Scholar 

  8. Berger, M., Ebin, D.: Some decompositions of the space of symmetric tensors on a Riemannian manifold. J. Differ. Geom.3, 379 (1969)

    Google Scholar 

  9. De Turck, D.: Correction to: Deforming metrics in the direction of the Ricci tensors (to appear)

  10. Friedman, A.: Partial differential equations of parabolic type. New York: Prentice-Hall 1964

    Google Scholar 

  11. Brézin, E., Hikama, S.: Three-loop calculations in the two-dimensional non-linear σ model. J. Phys. A11, 6, 1141 (1978)

    Google Scholar 

  12. Helgason, S.: Groups and geometric analysis. New York: Academic Press 1984

    Google Scholar 

  13. Reed, M., Simon, B.: Analysis of operators. New York: Academic Press 1978

    Google Scholar 

  14. Sullivan, D.: Related aspects of positivity. IHES preprint 1983

  15. Prat, J.: Etude asymptotique du mouvement Brownien sur une variété Riemannienne à courbure négative. C.R. Acad. Sci. Paris Sér. A–B272, A 1586 (1971)

    Google Scholar 

  16. Furstenberg, H.: Translation-invariant cones of functions on semi-simple Lie groups. Bull. Am. Math. Soc.71, 271 (1965)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. I.H.E.S., F-91440, Bures-sur-Yvette, France

    John Lott

Authors
  1. John Lott
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by A. Jaffe

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lott, J. Renormalization group flow for general σ-models. Commun.Math. Phys. 107, 165–176 (1986). https://doi.org/10.1007/BF01206956

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01206956

Keywords

Search

Navigation