The Chern-Simons coefficient in the Higgs phase (original) (raw)
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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.
The Chern-Simons Coefficient in Supersymmetric Non-abelian Chern-Simons Higgs Theories
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.
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.
Self-dual SU(3) Chern-Simons Higgs systems
Physical Review D, 1994
We explore self-dual Chern-Simons Higgs systems with the local SU(3) and global U(1) symmetries where the matter field lies in the adjoint representation.
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.
The Chern-Simons coefficient in supersymmetric Yang-Mills Chern-Simons theories
Physics Letters B, 1996
We study one-loop correction to the Chern-Simons coefficient κ = k/4π in N = 1, 2, 3 supersymmetric Yang-Mills Chern-Simons systems. In the pure bosonic case, the shift of the parameter k is known to be k → k + c v , where c v is the quadratic Casimir of the gauge group. In the N = 1 case, the fermionic contribution cancels the bosonic contribution by half and the shift is k → k + c v /2, making the theory anomalous if c v is odd. In the N = 2, 3 cases, the fermionic contribution cancels the bosonic contribution completely and there is no correction. We also calculate the mass corrections, showing the supersymmetry is preserved. As the matter fields decouple from the gauge field in the pure Chern-Simons limit, this work sheds some
Bose-Fermi Chern-Simons Dualities in the Higgsed Phase
JHEP 1811 (2018) 177
It has been conjectured that fermions minimally coupled to a Chern-Simons gauge field define a conformal field theory (CFT) that is level-rank dual to Chern-Simons gauged Wilson-Fisher Bosons. The CFTs in question admit relevant deformations parametrized by a real mass. When the mass deformation is positive, the duality of the two deformed theories has previously been checked in detail in the large N limit by comparing explicit all orders results on both sides of the duality. In this paper we perform a similar check for the case of negative mass deformations. In this case the bosonic field condenses triggering the Higgs mechanism. The effective excitations in this phase are massive W bosons. By summing all leading large N graphs involving these W bosons we find an all orders (in the 't Hooft coupling) result for the thermal free energy of the bosonic theory in the condensed phase. Our final answer perfectly matches the previously obtained fermionic free energy under the conjectured duality map.
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.
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.