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

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

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.

TWO-LOOP BETA-FUNCTION FOR NONLINEAR SIGMA-MODEL WITH AFFINE METRIC MANIFOLD

1994 ◽  
Vol 09 (26) ◽  
pp. 2411-2419 ◽  
Author(s):  
VASILY E. TARASOV
Keyword(s):  
Riemannian Manifolds ◽  
Sigma Model ◽  
Beta Function ◽  
Affine Connection ◽  
Dissipative System ◽  
Nonlinear Sigma Model ◽  
Two Dimensional ◽  
Invariance Condition ◽  
Target Manifold ◽  
Affine Metric

Two-loop metric counterterms for nonlinear two-dimensional bosonic σ-model with affine metric target manifold are calculated. The correlation of the metric and affine connection is derived from conformal invariance condition for nonlinear σ-model which is considered as a dissipative system. Examples of non-flat non-Riemannian manifolds resulting in trivial metric beta-function are suggested.

scholarly journals Solitons of Some Nonlinear Sigma-Like Models

2020 ◽  
Author(s):  
V.E. Vekslerchik ◽  
Keyword(s):  
Sigma Model ◽  
Soliton Solutions ◽  
Nonlinear Sigma Model ◽  
Two Dimensional ◽  
Differential Identities ◽  
Yang Mills ◽  
Class Of Matrices

We present a set of differential identities for some class of matrices. These identities are used to derive the N-soliton solutions for the Pohlmeyer nonlinear sigma-model, two-dimensional self-dual Yang-Mills equations and some modification of the vector Calapso equation.

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