scholarly journals Solving two-dimensional non-relativistic electronic and muonic atoms governed by Chern-Simons potential

2021 ◽  
Vol 127 ◽  
pp. 114521
Author(s):  
Francisco Caruso ◽  
José A. Helayël-Neto ◽  
Vitor Oguri ◽  
Felipe Silveira
Keyword(s):  
Two Dimensional ◽  
Muonic Atoms ◽  
Chern Simons

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.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

EQUIVALENCE OF TWO-DIMENSIONAL GRAVITIES

1990 ◽  
Vol 05 (16) ◽  
pp. 1251-1258 ◽  
Author(s):  
NOUREDDINE MOHAMMEDI
Keyword(s):  
Gauge Theory ◽  
Explicit Solution ◽  
Light Cone ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Dimensional Gravity ◽  
The Relationship ◽  
Chern Simons

We find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL (2, R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2+1 dimensional gravity. We present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given.

Bound state in a model of electromagnetic field interacting with a material plan

2020 ◽  
Vol 35 (21) ◽  
pp. 2050170
Author(s):  
Yu. M. Pismak ◽  
D. Shukhobodskaia
Keyword(s):  
Electromagnetic Field ◽  
Maxwell Equations ◽  
Singular Potential ◽  
Bound State ◽  
Material Object ◽  
Two Dimensional ◽  
Isotropic Plane ◽  
Chern Simons ◽  
Material Plane ◽  
State Of Field

In the model with Chern-Simons potential describing the coupling of electromagnetic field with a two-dimensional material, the possibility of the appearance of bound field states, vanishing at sufficiently large distances from interacting with its macro-objects, is considered. As an example of such two-dimensional material object we consider a homogeneous isotropic plane. Its interaction with electromagnetic field is described by a modified Maxwell equation with singular potential. The analysis of their solution shows that the bound state of field cannot arise without external charges and currents. In the model with currents and charges the Chern-Simons potential in the modified Maxwell equations creates bound state in the form of the electromagnetic wave propagating along the material plane with exponentially decreasing amplitude in the orthogonal to its direction.

scholarly journals Averaging over Narain moduli space

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Alexander Maloney ◽  
Edward Witten
Keyword(s):  
Einstein Gravity ◽  
Two Dimensions ◽  
Three Dimensions ◽  
One Dimension ◽  
Simons Theory ◽  
Two Dimensional ◽  
Dual Theory ◽  
Recent Developments ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract Recent developments involving JT gravity in two dimensions indicate that under some conditions, a gravitational path integral is dual to an average over an ensemble of boundary theories, rather than to a specific boundary theory. For an example in one dimension more, one would like to compare a random ensemble of two-dimensional CFT’s to Einstein gravity in three dimensions. But this is difficult. For a simpler problem, here we average over Narain’s family of two-dimensional CFT’s obtained by toroidal compactification. These theories are believed to be the most general ones with their central charges and abelian current algebra symmetries, so averaging over them means picking a random CFT with those properties. The average can be computed using the Siegel-Weil formula of number theory and has some properties suggestive of a bulk dual theory that would be an exotic theory of gravity in three dimensions. The bulk dual theory would be more like U(1)2D Chern-Simons theory than like Einstein gravity.

scholarly journals SCALING LIMITS OF THE CHERN–SIMONS–HIGGS ENERGY

2008 ◽  
Vol 10 (01) ◽  
pp. 1-16 ◽  
Author(s):  
MATTHIAS KURZKE ◽  
DANIEL SPIRN
Keyword(s):  
The Self ◽  
Scaling Limits ◽  
Gamma Convergence ◽  
Two Dimensional ◽  
Energy Formula ◽  
Simply Connected ◽  
Weak Topologies ◽  
Chern Simons ◽  
Dual Case ◽  
Dimensional Domain

We continue our study in [16] of the Gamma limit of the Abelian Chern–Simons–Higgs energy [Formula: see text] on a bounded, simply connected, two-dimensional domain where ε → 0 and με → μ ∈ [0, +∞]. Under the critical scaling, Gcsh ≈ | log ε2, we establish the Gamma limit when μ ∈ (0,+∞], and as a consequence, we are able to compute the first critical field H1 = H1(U,μ) for the nucleation of a vortex. Finally, we show failure of Gamma convergence when μμ → 0 (this includes the self-dual case). The method entails estimating in certain weak topologies the Jacobian J(uε) = det (∇ uε) in terms of the Chern–Simons–Higgs energy Ecsh.

Superconducting phase transition in a two-dimensional Chern-Simons theory

1991 ◽  
Vol 44 (14) ◽  
pp. 7519-7525 ◽  
Author(s):  
J. Kapusta ◽  
M. E. Carrington ◽  
B. Bayman ◽  
D. Seibert ◽  
C. S. Song
Keyword(s):  
Phase Transition ◽  
Superconducting Phase ◽  
Simons Theory ◽  
Two Dimensional ◽  
Chern Simons ◽  
Superconducting Phase Transition ◽  
Chern Simons Theory

Superfluidity of the Lattice Anyon Gas

1989 ◽  
Vol 03 (12) ◽  
pp. 1965-1995 ◽  
Author(s):  
Eduardo Fradkin
Keyword(s):  
Quantum Hall ◽  
Goldstone Mode ◽  
Two Dimensional ◽  
Hall Conductance ◽  
Dimensional Lattice ◽  
Quantum Hall Systems ◽  
Wigner Transformation ◽  
Topological Invariance ◽  
Quantum Hall System ◽  
Chern Simons

I consider a gas of “free” anyons with statistical paremeter δ on a two dimensional lattice. Using a recently derived Jordan-Wigner transformation, I map this problem onto a gas of fermions on a lattice coupled to a Chern-Simons gauge theory with coupling [Formula: see text]. I show that if [Formula: see text] and the density [Formula: see text], with r and q integers, the system is a superfluid. If q is even and the system is half filled the state may be either a superfluid or a Quantum Hall System depending on the dynamics. Similar conclusions apply for other values of ρ and δ. The dynamical stability of the Fetter-Hanna-Laughlin goldstone mode is insured by the topological invariance of the quantized Hall conductance of the fermion problem. This leads to the conclusion that anyon gases are generally superfluids or quantum Hall systems.

Twisted entropy functional for three-manifolds and flows induced on the boundary

2014 ◽  
Vol 11 (04) ◽  
pp. 1450033
Author(s):  
R. Cartas-Fuentevilla
Keyword(s):  
Diffusion Equation ◽  
Oscillatory Behavior ◽  
Two Dimensional ◽  
Manifolds With Boundary ◽  
Orthogonal Groups ◽  
Holonomy Groups ◽  
Entropy Functional ◽  
Chern Simons ◽  
Twisted Flows

Considering a twisted version of the gravitational Chern–Simons action for three-manifolds as a Perelman entropy functional, a generalization of the Cotton flow for the metric, in co-evolution with torsion is developed. In the case of manifolds with boundary, there exists an entropy functional induced on it, and hence metric and torsional flows can be defined. The integrability of these boundary flows is studied in detail. In a particular case, the solutions of the two-dimensional logarithmic diffusion equation determine completely the dynamics of the fields in co-evolution. In this scheme of three-manifolds with evolving boundaries, the orthogonality of the twisted flows to the Yamabe-like flows is established; additionally, the evolution of the holonomy groups of the three-manifold and of its boundary is studied, showing in some cases an oscillatory behavior around orthogonal groups. In this approach, the twisted canonical geometries (TCG) are defined as manifolds with a vanishing contribution of the torsion to the curvature, which will be generated fully by the metric; these geometries evolve to manifolds with curvature generated by both metric and torsion, and cannot smoothly evolve into manifolds with a vanishing torsion.

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