STABILITY OF NON-TOPOLOGICAL CHERN-SIMONS VORTICES IN A ϕ2-MODEL

1993 ◽  
Vol 08 (31) ◽  
pp. 2955-2962 ◽  
Author(s):  
JOAQUIN ESCALONA ◽  
MANUEL TORRES ◽  
ARMANDO ANTILLON
Keyword(s):  
Scalar Field ◽  
Gauge Fields ◽  
Magnetic Contribution ◽  
Small Perturbations ◽  
The Stability ◽  
Chern Simons ◽  
Topological Mass

We study the stability under small perturbations for the recently discovered self-dual non-topological vortices in a ϕ2 Abelian Chern-Simons (CS) theory. The solitons appear in the Bogomol'nyi limit of a model of scalar and gauge fields which includes both the CS term and an anomalous magnetic contribution. It is demonstrated here, that the vortices are stable or unstable according to whether the vector topological mass κ is less than or greater than the mass m of the scalar field. The interaction between vortices is determined as attractive for (m < κ) and repulsive for (m > κ).

ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Scalar Field ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Linear Equations ◽  
Dual Solutions ◽  
Gauge Fields ◽  
System Of Equations ◽  
Semisimple Lie Algebra ◽  
Yang Mills ◽  
Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

scholarly journals ON CANONICAL QUANTIZATION OF THE GAUGED WZW MODEL WITH PERMUTATION BRANES

2011 ◽  
Vol 26 (26) ◽  
pp. 4647-4660
Author(s):  
GOR SARKISSIAN
Keyword(s):  
Riemann Surface ◽  
Phase Space ◽  
Boundary Conditions ◽  
Canonical Quantization ◽  
Simons Theory ◽  
Gauge Fields ◽  
Time Line ◽  
Chern Simons ◽  
Special Case ◽  
Chern Simons Theory

In this paper we perform canonical quantization of the product of the gauged WZW models on a strip with boundary conditions specified by permutation branes. We show that the phase space of the N-fold product of the gauged WZW model G/H on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of the double Chern–Simons theory on a sphere with N holes times the time-line with G and H gauge fields both coupled to two Wilson lines. For the special case of the topological coset G/G we arrive at the conclusion that the phase space of the N-fold product of the topological coset G/G on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of Chern–Simons theory on a Riemann surface of the genus N-1 times the time-line with four Wilson lines.

scholarly journals THE EDGE STATES OF THE BF SYSTEM AND THE LONDON EQUATIONS

1993 ◽  
Vol 08 (04) ◽  
pp. 723-752 ◽  
Author(s):  
A.P. BALACHANDRAN ◽  
P. TEOTONIO-SOBRINHO
Keyword(s):  
Scalar Field ◽  
Scaling Limit ◽  
Quantum Hall ◽  
Simons Theory ◽  
Massless Scalar ◽  
Electromagnetic Current ◽  
Massless Scalar Field ◽  
Edge States ◽  
Chern Simons ◽  
London Equations

It is known that the 3D Chern–Simons interaction describes the scaling limit of a quantum Hall system and predicts edge currents in a sample with boundary, the currents generating a chiral U(1) Kac-Moody algebra. It is no doubt also recognized that, in a somewhat similar way, the 4D BF interaction (with B a two-form, dB the dual *j of the electromagnetic current, and F the electromagnetic field form) describes the scaling limit of a superconductor. We show in this paper that there are edge excitations in this model as well for manifolds with boundaries. They are the modes of a scalar field with invariance under the group of diffeomorphisms (diffeos) of the bounding spatial two-manifold. Not all diffeos of this group seem implementable by operators in quantum theory, the implementable group being a subgroup of volume-preserving diffeos. The BF system in this manner can lead to the w1+∞ algebra and its variants. Lagrangians for fields on the bounding manifold which account for the edge observables on quantization are also presented. They are the analogs of the (1+1)-dimensional massless scalar field Lagrangian describing the edge modes of an Abelian Chern-Simons theory with a disk as the spatial manifold. We argue that the addition of “Maxwell” terms constructed from F∧*F and dB∧*dB does not affect the edge states, and that the augmented Lagrangian has an infinite number of conserved charges—the aforementioned scalar field modes—localized at the edges. This Lagrangian is known to describe London equations and a massive vector field. A (3+1)-dimensional generalization of the Hall effect involving vortices coupled to B is also proposed.

scholarly journals Inflationary birefringence and baryogenesis

2016 ◽  
Vol 25 (11) ◽  
pp. 1640013 ◽  
Author(s):  
Stephon Alexander
Keyword(s):  
Gravitational Waves ◽  
Lepton Number ◽  
Gauge Fields ◽  
Lepton Asymmetry ◽  
Complex Phase ◽  
Inflaton Field ◽  
Model Based ◽  
Cross Correlations ◽  
Chern Simons

A decade ago, the first leptogenesis model based on inflation was proposed, where the complex phase of the inflaton field carries lepton number [S. H. S. Alexander, M. E. Peskin and M. M. Sheikh-Jabbari, Phys. Rev. Lett. 96 (2006) 081301, arXiv:hep-th/0403069 ]. If the inflaton field is an axion, it can couple to gravitational waves and gauge fields via Chern–Simons invariants. Due to these couplings, birefringent gravitational and gauge primordial perturbations are created during inflation to generate a lepton asymmetry, establishing a possible connection between nonvanishing TB-parity-violating polarization cross-correlations and leptogenesis. We also discuss the prospect for a subset of these models which can directly source circular (V-mode) polarization in the CMB.

scholarly journals Thick branes in the scalar–tensor representation of f(R, T) gravity

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
João Luís Rosa ◽  
Matheus A. Marques ◽  
Dionisio Bazeia ◽  
Francisco S. N. Lobo
Keyword(s):  
Scalar Field ◽  
Matter Field ◽  
Energy Tensor ◽  
Tensor Representation ◽  
Observable Universe ◽  
Brane Model ◽  
Gravitational Fields ◽  
Stress Energy ◽  
Tensor Representations ◽  
The Stability

AbstractBraneworld scenarios consider our observable universe as a brane embedded in a five-dimensional bulk. In this work, we consider thick braneworld systems in the recently proposed dynamically equivalent scalar–tensor representation of f(R, T) gravity, where R is the Ricci scalar and T the trace of the stress–energy tensor. In the general $$f\left( R,T\right) $$ f R , T case we consider two different models: a brane model without matter fields where the geometry is supported solely by the gravitational fields, and a second model where matter is described by a scalar field with a potential. The particular cases for which the function $$f\left( R,T\right) $$ f R , T is separable in the forms $$F\left( R\right) +T$$ F R + T and $$R+G\left( T\right) $$ R + G T , which give rise to scalar–tensor representations with a single auxiliary scalar field, are studied separately. The stability of the gravitational sector is investigated and the models are shown to be stable against small perturbations of the metric. Furthermore, we show that in the $$f\left( R,T\right) $$ f R , T model in the presence of an extra matter field, the shape of the graviton zero-mode develops internal structure under appropriate choices of the parameters of the model.

scholarly journals Massive scalar field perturbation on Kerr black holes in dynamical Chern–Simons gravity

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Shao-Jun Zhang
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Scalar Field ◽  
Massive Scalar ◽  
Coupling Constant ◽  
Field Mass ◽  
Field Perturbation ◽  
Massive Scalar Field ◽  
Kerr Black Holes ◽  
Chern Simons

AbstractWe study massive scalar field perturbation on Kerr black holes in dynamical Chern–Simons gravity by performing a $$(2+1)$$ ( 2 + 1 ) -dimensional simulation. Object pictures of the wave dynamics in time domain are obtained. The tachyonic instability is found to always occur for any nonzero black hole spin and any scalar field mass as long as the coupling constant exceeds a critical value. The presence of the mass term suppresses or even quench the instability. The quantitative dependence of the onset of the tachyonic instability on the coupling constant, the scalar field mass and the black hole spin is given numerically.

scholarly journals Corrigendum

1979 ◽  
Vol 22 (3) ◽  
pp. 571-572
Author(s):  
E. Infeld ◽  
G. Rowlands
Keyword(s):  
Large Amplitude ◽  
Plasma Waves ◽  
Relativistic Plasma ◽  
Small Perturbations ◽  
Transverse Waves ◽  
The Stability

In this note we investigate the stability of large-amplitude longitudinal relativistic plasma waves. We find that they are secularly stable, that is, small perturbations grow in time proportional to time but not exponentially with time. Similar results have recently been obtained for transverse waves by Romeiras (1978)

FERMI-BOSE TRANSMUTATIONS INDUCED BY GAUGE FIELDS

1988 ◽  
Vol 01 (11n12) ◽  
pp. 455-455 ◽  
Author(s):  
A.M. POLYAKOV
Keyword(s):  
Gauge Theory ◽  
Charged Particles ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Chern Simons

We show that in (2+1) -dimensional abelian gauge theory with the Chern-Simons term in the action, charged particles reverse their statistics.

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