scholarly journals On the topological charge conservation in the three-dimensional ${\rm O}(3)$ $\sigma$-model.

1984 ◽  
Vol 29 (5) ◽  
pp. 367-371
Author(s):  
Jaroslav Dittrich
Keyword(s):  
Topological Charge ◽  
Sigma Model ◽  
Three Dimensional ◽  
Charge Conservation

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.

Three-dimensional Dammann vortex array with tunable topological charge

2012 ◽  
Vol 51 (13) ◽  
pp. 2485 ◽  
Author(s):  
Junjie Yu ◽  
Changhe Zhou ◽  
Wei Jia ◽  
Anduo Hu ◽  
Wugang Cao ◽  
...  
Keyword(s):  
Topological Charge ◽  
Three Dimensional ◽  
Vortex Array

scholarly journals M and F Theory Instantons, N = 1 Supersymmetry and Fractional Topological Charge

1997 ◽  
Vol 12 (28) ◽  
pp. 5141-5149 ◽  
Author(s):  
César Gómez ◽  
Rafael Hernández
Keyword(s):  
Topological Charge ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Singular Points ◽  
Coulomb Branch ◽  
Supersymmetric Gauge Theories ◽  
Dimensional Theory ◽  
Pure Gauge ◽  
Supersymmetric Gauge

We analyze instanton generated superpotentials for three-dimensional N = 2 supersymmetric gauge theories obtained by compactifying on S1 N = 1 four-dimensional theories. For SU(2) with Nf = 1, we find that the vacua in the decompactification limit is given by the singular points of the Coulomb branch of the N = 2 four-dimensional theory (we also consider the massive case). The decompactification limit of the superpotential for pure gauge theories without chiral matter is interpreted in terms of 't Hooft's fractional instanton amplitudes.

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 Localized Kaluza-Klein 6-brane

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Tetsuji Kimura ◽  
Shin Sasaki ◽  
Kenta Shiozawa
Keyword(s):  
Gauge Theory ◽  
Sigma Model ◽  
Three Dimensional ◽  
Linear Sigma Model ◽  
Physical Origin ◽  
Fundamental String ◽  
Extended Space ◽  
Instanton Effect ◽  
M Theory ◽  
Kaluza Klein

Abstract We study the membrane wrapping mode corrections to the Kaluza-Klein (KK) 6-brane in eleven dimensions. We examine the localized KK6-brane in the extended space in E7(7) exceptional field theory. In order to discuss the physical origin of the localization in the extended space, we consider a probe M2-brane in eleven dimensions. We show that a three-dimensional $$ \mathcal{N} $$ N = 4 gauge theory is naturally interpreted as a membrane generalization of the two-dimensional $$ \mathcal{N} $$ N = (4, 4) gauged linear sigma model for the fundamental string. We point out that the vector field in the $$ \mathcal{N} $$ N = 4 model is identified as a dual coordinate of the KK6-brane geometry. We find that the BPS vortex in the gauge theory gives rise to the violation of the isometry along the dual direction. We then show that the vortex corrections are regarded as an instanton effect in M-theory induced by the probe M2-brane wrapping around the M-circle.

scholarly journals New Types of Three-Dimensional Vortices in the Heisenberg Model

2021 ◽  
Vol 122 (5) ◽  
pp. 423-427
Author(s):  
A. B. Borisov ◽  
D. V. Dolgikh
Keyword(s):  
Magnetic Structure ◽  
Topological Charge ◽  
Heisenberg Model ◽  
Three Dimensional ◽  
Geometric Interpretation ◽  
Vortex Filaments ◽  
Isotropic Magnet

Abstract The Heisenberg model for an isotropic magnet is considered in this work. A substitution that reduces the corresponding equations to equations with a simpler geometric interpretation is applied. One of the solutions of the latter describes a new magnetic structure comprised of two straight intersecting vortex filaments, which change the topological charge after intersection.

scholarly journals Gravitating superconducting solitons in the (3+1)-dimensional Einstein gauged non-linear $$\sigma $$-model

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Fabrizio Canfora ◽  
Alex Giacomini ◽  
Marcela Lagos ◽  
Seung Hun Oh ◽  
Aldo Vera
Keyword(s):  
Gravitational Lensing ◽  
Topological Charge ◽  
Sigma Model ◽  
Persistent Current ◽  
Linear Sigma Model ◽  
Dirac Monopole ◽  
Topological Solitons ◽  
Abelian Field ◽  
Non Linear ◽  
Fully Coupled

AbstractIn this paper, we construct the first analytic examples of $$(3+1)$$ ( 3 + 1 ) -dimensional self-gravitating regular cosmic tube solutions which are superconducting, free of curvature singularities and with non-trivial topological charge in the Einstein-SU(2) non-linear $$\sigma $$ σ -model. These gravitating topological solitons at a large distance from the axis look like a (boosted) cosmic string with an angular defect given by the parameters of the theory, and near the axis, the parameters of the solutions can be chosen so that the metric is singularity free and without angular defect. The curvature is concentrated on a tube around the axis. These solutions are similar to the Cohen–Kaplan global string but regular everywhere, and the non-linear $$\sigma $$ σ -model regularizes the gravitating global string in a similar way as a non-Abelian field regularizes the Dirac monopole. Also, these solutions can be promoted to those of the fully coupled Einstein–Maxwell non-linear $$\sigma $$ σ -model in which the non-linear $$\sigma $$ σ -model is minimally coupled both to the U(1) gauge field and to General Relativity. The analysis shows that these solutions behave as superconductors as they carry a persistent current even when the U(1) field vanishes. Such persistent current cannot be continuously deformed to zero as it is tied to the topological charge of the solutions themselves. The peculiar features of the gravitational lensing of these gravitating solitons are shortly discussed.

scholarly journals 4d Chern-Simons theory as a 3d Toda theory, and a 3d-2d correspondence

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Meer Ashwinkumar ◽  
Kee-Seng Png ◽  
Meng-Chwan Tan
Keyword(s):  
Moduli Space ◽  
Sigma Model ◽  
Three Dimensional ◽  
Simons Theory ◽  
Yang Mills ◽  
Pole Type ◽  
Type Boundary ◽  
Chern Simons ◽  
Manifold With Corners ◽  
Chern Simons Theory

Abstract We show that the four-dimensional Chern-Simons theory studied by Costello, Witten and Yamazaki, is, with Nahm pole-type boundary conditions, dual to a boundary theory that is a three-dimensional analogue of Toda theory with a novel 3d W-algebra symmetry. By embedding four-dimensional Chern-Simons theory in a partial twist of the five-dimensional maximally supersymmetric Yang-Mills theory on a manifold with corners, we argue that this three-dimensional Toda theory is dual to a two-dimensional topological sigma model with A-branes on the moduli space of solutions to the Bogomolny equations. This furnishes a novel 3d-2d correspondence, which, among other mathematical implications, also reveals that modules of the 3d W-algebra are modules for the quantized algebra of certain holomorphic functions on the Bogomolny moduli space.

scholarly journals THE EFFECTIVE LAGRANGIAN OF THREE DIMENSIONAL QUANTUM CHROMODYNAMICS

1992 ◽  
Vol 07 (32) ◽  
pp. 7989-8000 ◽  
Author(s):  
G. FERRETTI ◽  
S.G. RAJEEV ◽  
Z. YANG
Keyword(s):  
Quantum Chromodynamics ◽  
Sigma Model ◽  
Three Dimensional ◽  
Low Energy ◽  
Nonlinear Sigma Model ◽  
Flavor Symmetry ◽  
Energy Limit ◽  
Long Wavelength ◽  
Effective Lagrangian ◽  
Chern Simons

We consider the low energy limit of three dimensional quantum chromodynamics (QCD) with an even number of flavors. We show that parity is not spontaneously broken, but the global (flavor) symmetry is spontaneously broken. The low energy effective Lagrangian is a nonlinear sigma model on the Grassmannian. Some Chern-Simons terms are necessary in the Lagrangian to realize the discrete symmetries correctly. We consider also another parametrization of the low energy sector which leads to a three dimensional analogue of the Wess-Zumino-Witten-Novikov model. Since three dimensional QCD is believed to be a model for quantum antiferromagnetism, our effective Lagrangian can describe their long wavelength excitations (spin waves).

scholarly journals LOCAL CHARGED STATES OF THE GAUGE FIELD IN THREE-DIMENSIONAL MAXWELL-TYPE THEORIES

1996 ◽  
Vol 11 (24) ◽  
pp. 1985-1997 ◽  
Author(s):  
E.C. MARINQ
Keyword(s):  
Magnetic Flux ◽  
Gauge Field ◽  
Correlation Functions ◽  
Topological Charge ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Subsidiary Condition ◽  
Maxwell Theory ◽  
Gauge Invariant ◽  
Creation Operators

Gauge-invariant local creation operators of charged states are introduced and studied in pure gauge theories of the Maxwell-type in (2+1) dimensions. These states are usually unphysical because of the subsidiary condition imposed on the physical subspace by Gauss’ law. A dual Maxwell theory which possesses a topological electric charge is introduced. Pure electrodynamics lies in the sector where the topological charge identically vanishes. Charge bearing operators completely expressed in terms of the gauge field, however, can create physical states in the nontrivial topological sectors which thereby generalize QED. An order–disorder structure exists relating the charged operators and the magnetic flux creating (vortex) operators, both through commutation rules and correlation functions. The relevance of this structure for bosonization in 2+1 dimensions is discussed.

Sign in / Sign up

Export Citation Format

Share Document