scholarly journals Large N Limit on Langevin Equation: Two-Dimensional Nonlinear Sigma Model

1993 ◽  
Vol 89 (1) ◽  
pp. 275-279
Author(s):  
R. Mochizuki ◽  
K. Yoshida
Keyword(s):  
Langevin Equation ◽  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Two Dimensional ◽  
Large N

scholarly journals DYNAMICAL MASS GENERATION AND CRITICAL CURVATURE IN THE O(N) NONLINEAR SIGMA MODEL

1996 ◽  
Vol 11 (19) ◽  
pp. 1569-1578
Author(s):  
DAE-YUP SONG
Keyword(s):  
Sigma Model ◽  
Three Dimensional ◽  
Nonlinear Sigma Model ◽  
Mass Generation ◽  
Dynamical Mass ◽  
Large N ◽  
Static Einstein Universe ◽  
Critical Curvature ◽  
Second Order Phase Transition ◽  
Dynamical Mass Generation

The large-N nonlinear O(N) sigma model with the curvature coupled term ξRn2 is examined on a spacetime of R1×S2 topology (three-dimensional static Einstein universe). Making use of the cutoff method, we find the renormalized effective potential which shows that, for ξ>1/8, there is a second-order phase transition. Above the critical curvature, the dynamical mass generation does not take place even in the strong-coupled regime. The phase structure of the model on S2 is also discussed.

THE BOSONIC SIGMA MODEL ON A TOROIDAL SURFACE

2004 ◽  
Vol 19 (16) ◽  
pp. 2713-2720
Author(s):  
D. G. C. McKEON
Keyword(s):  
Riemannian Manifold ◽  
Sigma Model ◽  
Three Dimensional ◽  
The Other ◽  
Target Space ◽  
Dimensional Euclidean Space ◽  
Nonlinear Sigma Model ◽  
Two Dimensional ◽  
Toroidal Surface ◽  
Spherical Basis

The nonlinear sigma model with a two-dimensional basis space and an n-dimensional target space is considered. Two different basis spaces are considered; the first is an 0(2)×0(2) subspace of the 0(2,2) projective space related to the Minkowski basis space, and the other is a toroidal space embedded into three-dimensional Euclidean space, characterized by radii R and r. The target space is taken to be an arbitrarily curved Riemannian manifold. One-loop dependence on the renormalization induced scale μ is shown in the toroidal basis space to be the same as in a flat or spherical basis space.

scholarly journals Perturbative construction of the two-dimensional O(N) nonlinear sigma model with ERG

2017 ◽  
Vol 41 ◽  
pp. 244-255
Author(s):  
Bekir Can LÜTFÜOĞLU ◽  
Hidenori SONODA
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Two Dimensional

Villarceau foliated solitons in the two-dimensional O(3) nonlinear sigma model

2006 ◽  
Vol 57 (1) ◽  
pp. 177-192 ◽  
Author(s):  
Manuel Barros ◽  
Magdalena Caballero ◽  
Miguel Ortega
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Two Dimensional

scholarly journals Large N transition in the 2D SU(N)xSU(N) nonlinear sigma model.

2009 ◽  
Author(s):  
Rajamani Narayanan ◽  
Herbert Neuberger ◽  
Ettore Vicari
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Large N

scholarly journals HOPF TERM, LOOP ALGEBRAS AND THREE-DIMENSIONAL NAVIER-STOKES EQUATION

1993 ◽  
Vol 08 (28) ◽  
pp. 2677-2686 ◽  
Author(s):  
YUTAKA MATSUO
Keyword(s):  
Current Algebra ◽  
Sigma Model ◽  
Three Dimensional ◽  
Virasoro Algebra ◽  
Navier Stokes ◽  
Nonlinear Sigma Model ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Loop Algebras ◽  
Extrinsic Geometry

The dynamics of the three-dimensional perfect fluid is equivalent to the motion of vortex filaments or "strings." We study the action principle and find that it is described by the Hopf term of the nonlinear sigma model. The Poisson bracket structure is described by the loop algebra, for example, the Virasoro algebra or the analog of O(3) current algebra. As a string theory, it is quite different from the standard Nambu-Goto string in its coupling to the extrinsic geometry. We also analyze briefly the two-dimensional case and give some emphasis on the w1+∞ structure.

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