Self-dual SU(3) Chern-Simons Higgs systems (original) (raw)
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A generalized self-dual Chern-Simons Higgs theory
Letters in Mathematical Physics, 1991
In the recently discovered Chern-Slmons model, the reduction to a Bogomol'nyi bound or self-duality depends crucially on the specific form of the Higgs potential energy function, which is characterized by a ~b 6 type self-interaction. The purpose of this paper is to show that a much wider class of Higgs self-interaction may be allowed to achieve self-duality provided that the kinetic energy term of the Higgs scalar is suitably modified. The existence of topological multivortex solutions is also established. Furthermore, it 1s remarked that the Melssner effect may occur in the model.
Advances in High Energy Physics, 2016
We have studied the existence of self-dual solitonic solutions in a generalization of the Abelian Chern-Simons-Higgs model. Such a generalization introduces two different nonnegative functions,ω1(|ϕ|)andω(|ϕ|), which split the kinetic term of the Higgs field,|Dμϕ|2→ω1(|ϕ|)|D0ϕ|2-ω(|ϕ|)|Dkϕ|2, breaking explicitly the Lorentz covariance. We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whetherω(|ϕ|)∝β|ϕ|2β-2withβ≥1. The self-dual or Bogomolnyi equations produce an infinity number of soliton solutions by choosing conveniently the generalizing functionω1(|ϕ|)which must be able to provide a finite magnetic field. Also, we have shown that by properly choosing the generalizing functions it is possible to reproduce the Bogomolnyi equations of the Abelian Maxwell-Higgs and Chern-Simons-Higgs models. Finally, some new self-dual|ϕ|6-vortex solutions have been analyzed from both theoretical and numerical point of view.
Self-duality of three-dimensional Chern-Simons theory
Nuclear Physics B, 1991
We describe a precise self-duality relation between the electric charge and magneüc flux vortex sectors in the (2 + 1)-dimensional 71N gauge Higgs model with Chern-Simons term. The phase structure of this model is deduced using the self-duality . In particular, we find that the Chern-Simons term suppresses the confinement phase. Compact U(1) pure Chern-Simons theory corresponds to an N~x, infinite bare gauge coupling and zero bare mass limit. The self-duality of Chern-Simons theory is used to explain the hierarchy of odd-denominator filling fractions in the fractional quantum Hall effect and to seggest similar hierarchical ground-state structures in theories of the anyon and high-temperature superconductivity. Possible extensions to the nonabelian gauge groups and connection to the two-dimensional conformal field theories are also discussed .
Generalized self-dual Maxwell-Chern-Simons-Higgs model
Physical Review D, 2012
We present a consistent BPS framework for a generalized Maxwell-Chern-Simons-Higgs model. The overall model, including its self-dual potential, depends on three different functions, h (|φ| , N ), w (|φ|) and G (|φ|), which are functions of the scalar fields only. The BPS energy is proportional to the magnetic flux when w (|φ|) and G (|φ|) are related to each other by a differential constraint. We present an explicit non-standard model and its topologically non-trivial static configurations, which are described by the usual radially symmetric profile. Finally, we note that the non-standard results behave in a similar way as their standard counterparts, as expected, reinforcing the consistence of the overall construction.
Peculiar charged vortices in Higgs models with pure Chern-Simons term
Physics Letters B, 1990
We show that abelian as well as nonabelian Higgs models in (2+ 1) dimensions with the pure Chern-Simons term possess peculiar charged vortex solutions of finite energy. For all of them the magnetic field vanishes not only at infinity but also at the origin. Such objects can also be shown to exist in an abelian Higgs model without the Chern-Simons term but with non-minimal coupling.
The existence of non-topological solitons in the self-dual Chern-Simons theory
Communications in Mathematical Physics, 1992
In the recently discovered (2 + l)-dimensional relativistic Chern-Simons model, self-duality can be achieved when the Higgs potential density assumes a special form for which both the asymmetric and symmetric vacua are ground state solutions. This important feature may imply the coexistence of static topological and non-topological vortex-like solutions in R 2 but the latter have been rather elusive to a rigorous construction. Our main purpose in this paper is to prove the existence of non-topological radially symmetric iV-vortex solutions in the self-dual Chern-Simons model. By a shooting method, we obtain a continuous family of gauge-distinct Nvortex solutions. Moreover, we are also able to classify all possible bare (or 0-vortex) solutions.
Physical Review D
While the phase structure of the U (1) × U (1)-symmetric Higgs theory is still under debate, a version of this theory with an additional Chern-Simons term was recently shown to undergo a second-order phase transition [V. Shyta, J. van den Brink, and F. S. Nogueira, Phys. Rev. Lett. 127, 045701 (2021)]. This theory is dual to a topological field theory of massless fermions featuring two gauge fields. Here we elaborate on several aspects of this duality, focusing on the critical current correlators and on the nature of the critical point as reflected by the bosonization duality. The current correlators associated to the U (1) × U (1) symmetry and the topological current are shown to coincide up to a universal prefactor, which we find to be the same for both U (1) and U (1) × U (1) topological Higgs theories. The established duality offers in addition another way to substantiate the claim about the existence of a critical point in the bosonic Chern-Simons U (1) × U (1) Higgs model: a Schwinger-Dyson analysis of the fermionic dual model shows that no dynamical mass generation occurs. The same cannot be said for the theory without the Chern-Simons term in the action.
Vortex condensation in the Chern-Simons Higgs model: An existence theorem
Communications in Mathematical Physics, 1995
It is shown that there is a critical value of the Chern-Simons coupling parameter so that, below the value, there exists self-dual doubly periodic vortex solutions, and, above the value, the vortices are absent. Solutions of such a nature indicate the existence of dyon condensates carrying quantized electric and magnetic charges.
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The self-dual Chern-Simons CP(N) models
Physics Letters B, 1996
We study the Chern-Simons CP (N ) models with a global U (1) symmetry and found the self-dual models among them. The Bogomolnyi-type bound in these self-dual models is a nontrivial generalization of that in the pure CP (N ) models. Our models have quite a rich vacuum and soliton structure and approach the many known gauged self-dual models in some limit.
BPS domain wall solutions in self-dual Chern-Simons-Higgs systems
Physical Review D, 1997
We study domain wall solitons in the relativistic self-dual Chern-Simons-Higgs systems by the dimensional reduction method to two-dimensional spacetime. The Bogomol'nyi bound on the energy is given by two conserved quantities in a similar way that the energy bound for Bogomol'nyi-Prasad-Sommerfield (BPS) dyons is set in some Yang-Mills-Higgs systems in four dimensions. We find the explicit soliton configurations which saturate
Chern-Simons coefficient in supersymmetric non-Abelian Chern-Simons Higgs theories
Physical Review D, 1999
By taking into account the effect of the would be Chern-Simons term, we calculate the quantum correction to the Chern-Simons coefficient in supersymmetric Chern-Simons Higgs theories with matter fields in the fundamental representation of SU (n). Because of supersymmetry, the corrections in the symmetric and Higgs phases are identical. In particular, the correction is vanishing for N = 3 supersymmetric Chern-Simons Higgs theories. The result should be quite general, and have important implication for the more interesting case when the Higgs is in the adjoint representation.
Mass spectra of N=2 supersymmetric SU(n) Chern-Simons-Higgs theories
Physical Review D, 2001
An algebraic method is used to work out the mass spectra and symmetry breaking patterns of general vacuum states in N = 2 supersymmetric SU (n) Chern-Simons-Higgs systems with the matter fields being in the adjoint representation. The approach provides with us a natural basis for fields, which will be useful for further studies in the self-dual solutions and quantum corrections. As the vacuum states satisfy the SU (2) algebra, it is not surprising to find that their spectra are closely related to that of angular momentum addition in quantum mechanics. The analysis can be easily generalized to other classical Lie groups.
Non-Abelian Chern-Simons coefficient in the Higgs phase
Physical Review D, 1998
We calculate the one loop corrections to the Chern-Simons coe cient in the Higgs phase of Yang-Mills Chern-Simons Higgs theories. When the gauge group is S U N, we show, by taking into account the e ect of the would beChern-Simons term, that the corrections are always integer multiples of 1 4 , as they should for the theories to be quantum-mechanically consistent. In particular, the correction is vanishing for S U 2. The same method can also beapplied to the case that the gauge group is S O N. The result for S O 2 agrees with that found in the abelian Chern-Simons theories. Therefore, the calculation provides with us a uni ed understanding of the quantum correction to the Chern-Simons coe cient.
On Non-Topological Solutions for Planar Liouville Systems of Toda-Type
Communications in Mathematical Physics, 2016
Motivated by the study of non-abelian Chern Simons vortices of non-topological type in Gauge Field Theory, see e.g. [33, 34],[26], we analyse the solvability of the following (normalised) Liouville-type system in presence of singular sources: (1) τ −∆u 1 = e u1 − τ e u2 − 4N π δ 0 , −∆u 2 = e u2 − τ e u1 , β 1 = 1 2π R 2 e u1 and β 2 = 1 2π R 2 e u2 , with τ > 0 and N > 0. We identify necessary and sufficient conditions on the parameter τ and the "flux" pair: (β 1 , β 2), which ensure the radial solvability of (1) τ. Since for τ = 1 2 , problem (1) τ reduces to the (integrable) 2 X 2 Toda system, in particular we recover the existence result of [50] and [41], concerning this case. Our method relies on a blow-up analysis for solutions of (1) τ , which (even in the radial setting) takes new turns compared to the single equation case. We mention that our approach permits to handle also the non-symmetric case, where in each of the two equations in (1) τ , the parameter τ is replaced by two different parameters τ 1 > 0 and τ 2 > 0 respectively, and when also the second equation in (1) τ includes a Dirac measure supported at the origin.
B 2 and G2 Toda systems on compact surfaces: A variational approach
Journal of Mathematical Physics, 2017
We consider the B2 and G2 Toda systems on a compact surface (Σ, g), namely, systems of two Liouville-type PDEs coupled with a matrix of coefficients A=(aij)=2−1−22 or 2−1−32. We attack the problem using variational techniques, following the previous work [Battaglia, L. et al., Adv. Math. 285, 937–979 (2015)] concerning the A2 Toda system, namely, the case A=2−1−12. We get the existence and multiplicity of solutions as long as χ(Σ) ≤ 0 and a generic choice of the parameters. We also extend some of the results to the case of general systems.
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Mass spectra of N=2 supersymmetric SU(n) Chern-Simons-Higgs theories
Physical Review D, 2001
An algebraic method is used to work out the mass spectra and symmetry breaking patterns of general vacuum states in N = 2 supersymmetric SU (n) Chern-Simons-Higgs systems with the matter fields being in the adjoint representation. The approach provides with us a natural basis for fields, which will be useful for further studies in the self-dual solutions and quantum corrections. As the vacuum states satisfy the SU (2) algebra, it is not surprising to find that their spectra are closely related to that of angular momentum addition in quantum mechanics. The analysis can be easily generalized to other classical Lie groups.
Nontopological condensates for the self-dual Chern-Simons-Higgs Model
Communications on Pure and Applied Mathematics, 2014
For the abelian self-dual Chern-Simons-Higgs model we address existence issues of periodic vortex configurations -the so-called condensates-of non-topological type as k → 0, where k > 0 is the Chern-Simons parameter. We provide a positive answer to the long-standing problem on the existence of non-topological condensates with magnetic field concentrated at some of the vortex points (as a sum of Dirac measures) as k → 0, a question which is of definite physical interest.
Vortices in Higgs models with and without Chern-Simons terms
Physics Letters B, 1989
We note that neutrl vortices in a fermionic background acquire the same local charge and spin quantum numbers as charged vortices in a Chern-Simons theory, provided the Chern-Simons mass is obtained by integrating out the fermions. We also point out that in an SU(2) theory involving (globally) charged fermions, (globally) neutral fermions appear as pairs of Z2 solitons and comment on their relevance to condensed matter systems.
On the solitons of the Chern-Simons-Higgs model
The European Physical Journal C, 1999
Several issues concerning the self-dual solutions of the Chern-Simons-Higgs model are addressed. The topology of the configuration space of the model is analysed when the space manifold is either the plane or an infinite cylinder. We study the local structure of the moduli space of self-dual solitons in the second case by means of an index computation. It is shown how to manage the non-integer contribution to the heat-kernel supertrace due to the non-compactness of the base space. A physical picture of the local coordinates parametrizing the non-topological soliton moduli space arises .
SELF-DUAL SOLITONS IN N=2 SUPERSYMMETRIC SEMILOCAL CHERN–SIMONS THEORY
Modern Physics Letters A, 1998
We embed the semilocal Chern-Simons-Higgs theory into an N = 2 supersymmetric system. We construct the corresponding conserved supercharges and derive the Bogomol'nyi equations of the model from supersymmetry considerations. We show that these equations hold provided certain conditions on the coupling constants as well as on the Higgs potential of the system, which are a consequence of the huge symmetry of the theory, are satisfied. They admit string-like solutions which break one half of the supersymmetries -BPS Chern-Simons semilocal cosmic strings-whose magnetic flux is concentrated at the center of the vortex. We study such solutions and show that their stability is provided by supersymmetry through the existence of a lower bound for the energy, even though the manifold of the Higgs vacuum does not contain non-contractible loops.
Generalized self-duality for the Yang-Mills-Higgs system
Physical Review D, 2021
Self-duality is a very important concept in the study and applications of topological solitons in many areas of Physics. The rich mathematical structures underlying it lead, in many cases, to the development of exact and non-perturbative methods. We present a generalization of the Yang-Mills-Higgs system by the introduction of scalar fields assembled in a symmetric and invertible matrix h of the same dimension as the gauge group. The coupling of such new fields to the gauge and Higgs fields is made by replacing the Killing form, in the contraction of the group indices, by the matrix h in the kinetic term for the gauge fields, and by its inverse in the Higgs field kinetic term. The theory is conformally invariant in the three dimensional space IR 3. An important aspect of the model is that for practically all configurations of the gauge and Higgs fields the new scalar fields adjust themselves to solve the modified self-duality equations. We construct solutions using a spherically symmetric ansätz and show that the 't Hooft-Polyakov monopole becomes a self-dual solution of such modified Yang-Mills-Higgs system. We use an ansätz based on the conformal symmetry to construct vacuum solutions presenting non-trivial toroidal magnetic fields.
Self-dual Maxwell–Chern–Simons solitons from a Lorentz-violating model
Physics Letters B, 2013
Self-dual abelian Higgs system, involving both the Maxwell and Chern-Simons terms are obtained from Carroll-Field-Jackiw theory by dimensional reduction. Bogomol'nyi-type equations are studied from theoretical and numerical point of view. In particular we show that the solutions of these equations are Nielsen-Olesen vortices with electric charge.
The Chern-Simons coefficient in the Higgs phase
Physics Letters B, 1994
We study one-loop corrections to the Chern-Simons coefficient κ in abelian self-dual Chern-Simons Higgs systems and their N = 2 and N = 3 supersymmetric generalizations in both symmetric and asymmetric phases. One-loop corrections to the Chern-Simons coefficient of these systems turn out to be integer multiples of 1/4π in both phases. Especially in the maximally supersymmetric N = 3 case, the correction in symmetric phase vanishes and that in asymmetric phase is κ/(2π|κ|). Our results suggest that nonabelian self-dual systems might enjoy similar features.
The BPS Domain Wall Solutions in Self-Dual Chern-Simons-Higgs Systems
Physical Review D
We study domain wall solitons in the relativistic self-dual Chern-Simons Higgs systems by the dimensional reduction method to two dimensional spacetime. The Bogomolny bound on the energy is given by two conserved quantities in a similar way that the energy bound for BPS dyons is set in some Yang-Mills-Higgs systems in four dimensions.
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