scholarly journals TOROIDAL SOLITON SOLUTIONS IN O(3)N NONLINEAR SIGMA MODEL

2004 ◽  
Vol 19 (34) ◽  
pp. 2569-2578 ◽  
Author(s):  
A. WERESZCZYŃSKI
Keyword(s):  
Sigma Model ◽  
Soliton Solutions ◽  
Minkowski Spacetime ◽  
Scalar Fields ◽  
Repulsive Interaction ◽  
Nonlinear Sigma Model ◽  
Nonlinear Coupling ◽  
Highly Nonlinear

A set of N three-component unit scalar fields in (3+1) Minkowski spacetime is investigated. The highly nonlinear coupling between them is chosen to omit the scaling instabilities. The multi-soliton static configurations with arbitrary Hopf numbers are found. Moreover, the generalized version of the Vakulenko–Kapitansky inequality is obtained. The possibility of attractive as well as repulsive interaction between hopfions is shown. A noninteracting limit is also discussed.

scholarly journals Higgs inflation as nonlinear sigma model and scalaron as its σ-meson

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yohei Ema ◽  
Kyohei Mukaida ◽  
Jorinde van de Vis
Keyword(s):  
Sigma Model ◽  
Planck Scale ◽  
Scalar Fields ◽  
Target Space ◽  
Linear Sigma Model ◽  
Nonlinear Sigma Model ◽  
Jordan Frame ◽  
Quadratic Gravity ◽  
Frame Transformation ◽  
Definition Of

Abstract We point out that a model with scalar fields with a large nonminimal coupling to the Ricci scalar, such as Higgs inflation, can be regarded as a nonlinear sigma model (NLSM). With the inclusion of not only the scalar fields but also the conformal mode of the metric, our definition of the target space of the NLSM is invariant under the frame transformation. We show that the σ-meson that linearizes this NLSM to be a linear sigma model (LSM) corresponds to the scalaron, the degree of freedom associated to the R2 term in the Jordan frame. We demonstrate that quantum corrections inevitably induce this σ-meson in the large-N limit, thus providing a frame independent picture for the emergence of the scalaron. The resultant LSM only involves renormalizable interactions and hence its perturbative unitarity holds up to the Planck scale unless it hits a Landau pole, which is in agreement with the renormalizability of quadratic gravity.

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.

BULK SCALAR-FIELD INFLUENCED FRW UNIVERSE MODEL

2012 ◽  
Vol 27 (01) ◽  
pp. 1250003 ◽  
Author(s):  
TAE HOON LEE ◽  
SUNNYEO LEE
Keyword(s):  
Sigma Model ◽  
Scalar Fields ◽  
Einstein Gravity ◽  
Warp Factor ◽  
Nonlinear Sigma Model ◽  
Universe Model ◽  
Frw Universe ◽  
Brane Model ◽  
Bulk Scalar Field ◽  
The One

We consider a nonlinear sigma-model-like theory of bulk scalar fields coupled to the five-dimensional Einstein gravity. In Robertson–Walker spacetimes, we find some power-law cosmological solutions for the scale factor when the expansion rate of an extra dimension is proportional to one of our (3+1)-dimensional universe. Among them, the solution with a decreasing warp factor could be related to the one-brane model of Randall and Sundrum.

scholarly journals ON THE GAUGED NONCOMPACT SPIN SYSTEM

1998 ◽  
Vol 13 (32) ◽  
pp. 5503-5517
Author(s):  
SUNG-SOO KIM ◽  
PHILLIAL OH
Keyword(s):  
Spin System ◽  
Sigma Model ◽  
Soliton Solutions ◽  
Finite Energy ◽  
Nonlinear Sigma Model ◽  
Rotationally Symmetric ◽  
Background Charge ◽  
Chern Simons ◽  
Symmetric Soliton ◽  
Naive Model

We examine classical and quantum aspects of the planar noncompact spin system coupled with Chern–Simons gauge field in the presence of background charge. We first define our classical spin system as nonrelativistic nonlinear sigma model in which the order parameter spin takes value in the noncompact manifold ℳ= SU(1, 1)/U(1) . Although the naive model does not allow any finite energy self-dual solitons, it is shown that the gauged system admits static Bogomol'nyi solitons with finite energy whose rotationally symmetric soliton solutions are analyzed in detail. We also discuss the large spin limit in which the self-dual equation reduces to the well-known gauged nonlinear Schrödinger model or Abelian Higgs model, depending on the choice of the background charge term. Then, we perform quantization of the model. We find that the spin algebra satisfies anomalous commutation relations, and the system is a field theoretic realization of the anyons.

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

scholarly journals An emergent universe supported by a nonlinear sigma model

2009 ◽  
Vol 26 (7) ◽  
pp. 075017 ◽  
Author(s):  
A Beesham ◽  
S V Chervon ◽  
S D Maharaj
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Emergent Universe

scholarly journals Isolated skyrmions in the CP2 nonlinear sigma model with a Dzyaloshinskii-Moriya type interaction

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Yutaka Akagi ◽  
Yuki Amari ◽  
Nobuyuki Sawado ◽  
Yakov Shnir
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Type Interaction
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