scholarly journals Matter in 2+1 Dimensions at Finite Density with Chern Simons Interactions

2020 ◽  
Author(s):  
◽  
Stanislav Stratiev
Keyword(s):  
Ground State ◽  
Particle Number ◽  
Chemical Potential ◽  
Vacuum Expectation ◽  
Simons Theory ◽  
Vortex Solutions ◽  
Scalar Potentials ◽  
Chern Simons ◽  
Do So ◽  
Chern Simons Theory

We study several matter Chern-Simons models at finite chemical potential. In the SU(N) theory we discover a colour-flavour locked Bose condensed ground state with vacuum expectation values for both the scalar and gauge fields. We identify this ground state with the non-commutative Chern-Simons description of the quan-tum Hall eect. We compute the quadratic spectrum and discover roton excitations. We find a self-consistent circularly symmetric ansatz for topological non-abelian vortices. We examine vortices in abelian Chern-Simons theory coupled to a relativistic scalar field with a chemical potential for particle number or U(1) charge. The Gauss constraint requires chemical potential for the local symme-try to be accompanied by a constant background charge density/ma-gnetic field. Focusing attention on power law scalar potentials |Φ|2s, s ∈ Z, which do not support vortex configurations in vacuum but do so at finite chemical potential, we numerically study classical vortex solutions for a large winding number |n|  1.

CHERN-SIMONS THEORY, MODULAR FUNCTIONS AND QUANTUM MECHANICS IN AN ALCOVE

1991 ◽  
Vol 06 (10) ◽  
pp. 1815-1827 ◽  
Author(s):  
SHAHN MAJID ◽  
YA. S. SOIBELMAN
Keyword(s):  
Regular Representation ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Simons Theory ◽  
Mathematical Work ◽  
Modular Functions ◽  
Left Regular Representation ◽  
Left Regular ◽  
Chern Simons ◽  
Chern Simons Theory

We show how the vacuum expectation value of the Wilson loop of the trivial knot in the left-regular representation in a Chern-Simons theory is basically the partition function for a quantum particle confined to a certain bounded region (namely, an alcove of the gauge group Lie algebra). For example, for su(3) the particle is confined to an equilateral triangle. The result follows from mathematical work on the category-theoretic rank of quantum groups obtained in a previous paper. In the present paper we give the details of the physical interpretation and discuss the implications. In particular, both these physical systems are connected with number theory.

scholarly journals Vortex solutions of the Lifshitz-Chern-Simons theory

2013 ◽  
Vol 87 (2) ◽  
Author(s):  
N. Grandi ◽  
I. Salazar Landea ◽  
G. A. Silva
Keyword(s):  
Simons Theory ◽  
Vortex Solutions ◽  
Chern Simons ◽  
Chern Simons Theory

TOPOLOGICAL ORDERS AND CHERN-SIMONS THEORY IN STRONGLY CORRELATED QUANTUM LIQUID

1991 ◽  
Vol 05 (10) ◽  
pp. 1641-1648 ◽  
Author(s):  
XIAO-GANG WEN
Keyword(s):  
Ground State ◽  
Simons Theory ◽  
Strongly Correlated ◽  
Quantum Liquid ◽  
Quantum Liquids ◽  
Ground State Degeneracy ◽  
Chern Simons ◽  
Chern Simons Theory

We review the topological orders in strongly correlated quantum liquids. The characterization of the topological orders through ground state degeneracy, non-Abelian Berry's phases and edge excitations are discussed.

ANYONIZATION AND SUPERFLUIDITY OF LATTICE CHERN-SIMONS THEORY

1992 ◽  
Vol 07 (06) ◽  
pp. 513-520 ◽  
Author(s):  
D. ELIEZER ◽  
G.W. SEMENOFF ◽  
S.S.C. WU
Keyword(s):  
Long Range ◽  
Ground State ◽  
Hamiltonian Formalism ◽  
Range Order ◽  
Simons Theory ◽  
Long Range Order ◽  
Flux Tubes ◽  
Gauge Transformations ◽  
Chern Simons ◽  
Chern Simons Theory

We prove, working in the Hamiltonian formalism, that a U(1) Chern-Simons theory coupled to fermions on a lattice can be mapped exactly onto a theory of interacting lattice anyons. This map does not involve any singular gauge transformations, and is everywhere well defined. We also prove that, when the statistics parameter is an odd integer so that the anyons are bosons, the ground state, which consists of a condensate of bound pairs of flux tubes and fermions, breaks phase invariance. The ensuing long range order implies that the system is an unconventional superfluid.

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 Wilson-’t Hooft lines as transfer matrices

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kazunobu Maruyoshi ◽  
Toshihiro Ota ◽  
Junya Yagi
Keyword(s):  
Vacuum Expectation ◽  
Simons Theory ◽  
Transfer Matrices ◽  
Quantum Integrable Systems ◽  
Expectation Values ◽  
Twisted Product ◽  
Agt Correspondence ◽  
Supersymmetric Gauge ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We establish a correspondence between a class of Wilson-’t Hooft lines in four-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for trigonometric quantum integrable systems. We compute the vacuum expectation values of the Wilson-’t Hooft lines in a twisted product space S1 × ϵ ℝ2 × ℝ by supersymmetric localization and show that they are equal to the Wigner transforms of the transfer matrices. A variant of the AGT correspondence implies an identification of the transfer matrices with Verlinde operators in Toda theory, which we also verify. We explain how these field theory setups are related to four-dimensional Chern-Simons theory via embedding into string theory and dualities.

scholarly journals CHERN–SIMONS THEORY, EXACTLY SOLVABLE MODELS AND FREE FERMIONS AT FINITE TEMPERATURE

2009 ◽  
Vol 24 (39) ◽  
pp. 3157-3171 ◽  
Author(s):  
MIGUEL TIERZ
Keyword(s):  
Ground State ◽  
Finite Temperature ◽  
Simons Theory ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Free Fermions ◽  
Exactly Solvable ◽  
The Relationship ◽  
Chern Simons ◽  
Chern Simons Theory

We show that matrix models in Chern–Simons theory admit an interpretation as 1D exactly solvable models, paralleling the relationship between the Gaussian model and the Calogero model. We compute the corresponding Hamiltonians, ground-state wave functions and ground-state energies and point out that the models can be interpreted as quasi-1D Coulomb plasmas. We also study the relationship between Chern–Simons theory on S3 and a system of N one-dimensional fermions at finite temperature with harmonic confinement. In particular, we show that the Chern–Simons partition function can be described by the density matrix of the free fermions in a very particular, crystalline, configuration. For this, we both use the Brownian motion and the matrix model description of Chern–Simons theory and find several common features with c = 1 theory at finite temperature. Finally, using the exactly solvable model result, we show that the finite temperature effect can be described with a specific two-body interaction term in the Hamiltonian, with 1D Coulombic behavior at large separations.

scholarly journals GAUGE DEPENDENCE IN CHERN–SIMONS THEORY

1999 ◽  
Vol 14 (03) ◽  
pp. 463-479 ◽  
Author(s):  
F. A. DILKES ◽  
L. C. MARTIN ◽  
D. G. C. MCKEON ◽  
T. N. SHERRY
Keyword(s):  
Proper Time ◽  
Three Dimensional ◽  
Vacuum Expectation ◽  
Three Dimensions ◽  
Simons Theory ◽  
Gauge Parameter ◽  
Gauge Dependence ◽  
Gauge Fixing ◽  
Chern Simons ◽  
Chern Simons Theory

We compute the contribution to the modulus of the one-loop effective action in pure non-Abelian Chern–Simons theory in an arbitrary covariant gauge. We find that the results are dependent on both the gauge parameter (α) and the metric required in the gauge fixing. A contribution arises that has not been previously encountered; it is of the form [Formula: see text]. This is possible as in three dimensions α is dimensionful. A variant of proper time regularization is used to render these integrals well behaved (although no divergences occur when the regularization is turned off at the end of the calculation). Since the original Lagrangian is unaltered in this approach, no symmetries of the classical theory are explicitly broken and ∊μλν is handled unambiguously since the system is three-dimensional at all stages of the calculation. The results are shown to be consistent with the so-called Nielsen identities which predict the explicit gauge parameter dependence using an extension of BRS symmetry. We demonstrate that this α dependence may potentially contribute to the vacuum expectation values of products of Wilson loops.

scholarly journals AREA PRESERVING DIFFEOMORPHISMS AND W∞ SYMMETRY IN A 2+1 CHERN-SIMONS THEORY

1992 ◽  
Vol 07 (40) ◽  
pp. 3717-3730 ◽  
Author(s):  
IAN I. KOGAN
Keyword(s):  
Gauge Theory ◽  
Phase Space ◽  
String Theory ◽  
Ground State ◽  
Simons Theory ◽  
Canonical Transformations ◽  
Discrete States ◽  
Chern Simons ◽  
Area Preserving ◽  
Chern Simons Theory

We discuss the W∞ symmetry in the 2+1 gauge theory with the Chern-Simons term. It is shown that the generators of this symmetry act on the ground state as the canonical transformations in the phase space. We shall also discuss the analogy between discrete states in c=1 string theory and Landau level states in 2+1 gauge theory with Chern-Simons term.

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