Stability of the (Two-Loop) Renormalization Group Flow for Nonlinear Sigma Models

被引：0
作者：
Christine Guenther
Todd A. Oliynyk
机构：
[1] Pacific University,Department of Mathematics and Computer Science
[2] Monash University,School of Mathematical Sciences
来源：
Letters in Mathematical Physics | 2008年 / 84卷
关键词：
35K55; 53C80; 58Z05; 81T17; renormalization group flow; Ricci flow; nonlinear stability;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove the stability of the torus, and with suitable rescaling, hyperbolic space under the (two-loop) renormalization group flow for the nonlinear sigma model. To prove stability we use similar techniques to Guenther et al. (Commun. Anal. Geom. 10:741–777, 2002), where the stability of the torus under Ricci flow was first established. The main technical tool is maximal regularity theory.
引用
收藏
页码：149 / 157
页数：8
相关论文
共 27 条
  • [1] Da Prato G.(1979)Equations d’évolution abstraites non linéaires de type parabolique, (French) Ann. Math. Pura Appl. 120 329-396
  • [2] Grisvard P.(1988)Stability, instability and center manifold theorem for fully nonlinear autonomous parabolic equations in Banach space Arch. Ration. Mech. Anal. 101 115-141
  • [3] Da Prato G.(1985)Nonlinear models in Ann. Phys. 163 318-419
  • [4] Lunardi A.(1985) dimensions Commun. Math. Phys 102 1-30
  • [5] Friedan D.(2002)Gross-Neveu model through convergent perturbation expansions Commun. Anal. Geom. 10 741-777
  • [6] Gawedzki K.(1982)Stability of the Ricci flow at Ricci-flat metrics J. Differ. Geom. 17 255-306
  • [7] Kupianinen A.(1989)Three-manifolds with positive Ricci curvature Nucl. Phys. B322 431-470
  • [8] Guenther C.(1979)A four-loop caclulation of the metric Osaka J. Math. 16 413-421
  • [9] Isenberg J.(1986)-function for the bosonic Commun. Math. Phys. 107 165-176
  • [10] Knopf D.(2005)-model and the string effective action Phys. Lett. B 610 115-121
123