TOPOLOGICAL HIGGS MECHANISM WITH ORDINARY HIGGS MECHANISM

1991 ◽  
Vol 06 (04) ◽  
pp. 295-302 ◽  
Author(s):  
ICHIRO ODA ◽  
SHIGEAKI YAHIKOZAWA
Keyword(s):  
Higher Dimensions ◽  
Higgs Mechanism ◽  
Simons Theory ◽  
Higgs Potential ◽  
Mass Generation ◽  
3 Dimensional ◽  
Chern Simons ◽  
Topological Mass ◽  
Chern Simons Theory ◽  
Topological Term

Topological Higgs mechanism in higher dimensions is analyzed when ordinary Higgs potential exists. It is shown that if 1-form B field becomes massive by the ordinary Higgs mechanism, another D-2 form C field also becomes massive through topological term in addition to the topological mass generation by the topological Higgs mechanism. Moreover, we investigate this mechanism in 3-dimensional theories, that is to say, Chern-Simons theory and more general theory.

scholarly journals SELF-DUAL SOLITONS IN N=2 SUPERSYMMETRIC SEMILOCAL CHERN–SIMONS THEORY

1998 ◽  
Vol 13 (21) ◽  
pp. 1689-1697
Author(s):  
JOSÉ D. EDELSTEIN
Keyword(s):  
Lower Bound ◽  
Magnetic Flux ◽  
Cosmic Strings ◽  
Coupling Constants ◽  
Simons Theory ◽  
Higgs Potential ◽  
Higgs Vacuum ◽  
Chern Simons ◽  
Chern Simons Theory

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 shown 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.

scholarly journals Geometric aspects of interpolating gauge-fixing in Chern–Simons theory

2018 ◽  
Vol 33 (02) ◽  
pp. 1850012
Author(s):  
Laurent Gallot ◽  
Philippe Mathieu ◽  
Éric Pilon ◽  
Frank Thuillier
Keyword(s):  
Simons Theory ◽  
3 Dimensional ◽  
Linking Number ◽  
Gauge Fixing ◽  
Covariant Gauge ◽  
Chern Simons ◽  
Chern Simons Theory

In this paper we investigate an interpolating gauge-fixing procedure in (4l + 3)-dimensional Abelian Chern–Simons theory. We show that this interpolating gauge is related to the covariant gauge in a constant anisotropic metric. We compute the corresponding propagators involved in various expressions of the linking number in various gauges. We comment on the geometric interpretations of these expressions, clarifying how to pass from one interpretation to another.

scholarly journals Introduction to Chern-Simons Theory

2020 ◽  
Author(s):  
Adémọ́lá Adéìfẹ́ọba
Keyword(s):  
Quantum Hall ◽  
Simons Theory ◽  
Yang Mills ◽  
Jones Polynomials ◽  
Interaction Term ◽  
Quantum Hall System ◽  
Chern Simons ◽  
Theoretic Description ◽  
Chern Simons Theory ◽  
Topological Term

The 2 + 1 Yang-Mills theory allows for an interaction term called the Chern-Simons term. This topological term plays a useful role in understanding the field theoretic description of the excitation of the quantum hall system such as Anyons. While solving the non-Abelian Chern-simons theory is rather complicated, its knotty world allows for a framework for solving it. In the framework, the idea was to relate physical observables with the Jones polynomials. In this note, I will summarize the basic idea leading up to this framework.

BOGOMOL’NYI EQUATIONS FOR NON-ABELIAN CHERN-SIMONS-HIGGS THEORIES

1991 ◽  
Vol 06 (06) ◽  
pp. 479-486 ◽  
Author(s):  
L.F. CUGLIANDOLO ◽  
G. LOZANO ◽  
M.V. MANÍAS ◽  
F.A. SCHAPOSNIK
Keyword(s):  
Angular Momentum ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Simons Theory ◽  
Higgs Potential ◽  
Topological Sector ◽  
Straightforward Generalization ◽  
Vortex Solutions ◽  
Chern Simons ◽  
Chern Simons Theory

We study the non-abelian Chern-Simons theory with spontaneous symmetry breaking. We find Bogomol’nyi type or self-dual equations for a particular choice of the Higgs potential; the corresponding vortex solutions for G=SU(2) carry both quantized electric charge Q= −en/2 and angular momentum J=nm2/4 (e is the fundamental charge, n is an integer associated with the Chern-Simons coefficient, and m is another integer which labels the topological sector). We propose a straightforward generalization to the SU(N) case.

scholarly journals Holst-MacDowell-Mansouri action for (extended) supergravity with boundaries and super Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
K. Eder ◽  
H. Sahlmann
Keyword(s):  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Chiral Limit ◽  
Geometric Approach ◽  
Simons Theory ◽  
New Developments ◽  
Yang Mills ◽  
Chern Simons ◽  
Chern Simons Theory ◽  
Topological Term

Abstract In this article, the Cartan geometric approach toward (extended) supergravity in the presence of boundaries will be discussed. In particular, based on new developments in this field, we will derive the Holst variant of the MacDowell-Mansouri action for $$ \mathcal{N} $$ N = 1 and $$ \mathcal{N} $$ N = 2 pure AdS supergravity in D = 4 for arbitrary Barbero-Immirzi parameters. This action turns out to play a crucial role in context of boundaries in the framework of supergravity if one imposes supersymmetry invariance at the boundary. For the $$ \mathcal{N} $$ N = 2 case, it follows that this amounts to the introduction of a θ-topological term to the Yang-Mills sector which explicitly depends on the Barbero-Immirzi parameter. This shows the close connection between this parameter and the θ-ambiguity of gauge theory.We will also discuss the chiral limit of the theory, which turns out to possess some very special properties such as the manifest invariance of the resulting action under an enlarged gauge symmetry. Moreover, we will show that demanding supersymmetry invariance at the boundary yields a unique boundary term corresponding to a super Chern-Simons theory with OSp($$ \mathcal{N} $$ N |2) gauge group. In this context, we will also derive boundary conditions that couple boundary and bulk degrees of freedom and show equivalence to the results found in the D’Auria-Fré approach in context of the non-chiral theory. These results provide a step towards of quantum description of supersymmetric black holes in the framework of loop quantum gravity.

Chern-Simons theory for electrons in high Landau levels

1999 ◽  
Vol 09 (PR10) ◽  
pp. Pr10-223-Pr10-225
Author(s):  
S. Scheidl ◽  
B. Rosenow
Keyword(s):  
Landau Levels ◽  
Simons Theory ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Field ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

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