scholarly journals Phase space structure of Chern–Simons theory with a non-standard puncture

2006 ◽  
Vol 738 (3) ◽  
pp. 425-456 ◽  
Author(s):  
C. Meusburger ◽  
B.J. Schroers
Keyword(s):  
Phase Space ◽  
Space Structure ◽  
Simons Theory ◽  
Phase Space Structure ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals ON CANONICAL QUANTIZATION OF THE GAUGED WZW MODEL WITH PERMUTATION BRANES

2011 ◽  
Vol 26 (26) ◽  
pp. 4647-4660
Author(s):  
GOR SARKISSIAN
Keyword(s):  
Riemann Surface ◽  
Phase Space ◽  
Boundary Conditions ◽  
Canonical Quantization ◽  
Simons Theory ◽  
Gauge Fields ◽  
Time Line ◽  
Chern Simons ◽  
Special Case ◽  
Chern Simons Theory

In this paper we perform canonical quantization of the product of the gauged WZW models on a strip with boundary conditions specified by permutation branes. We show that the phase space of the N-fold product of the gauged WZW model G/H on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of the double Chern–Simons theory on a sphere with N holes times the time-line with G and H gauge fields both coupled to two Wilson lines. For the special case of the topological coset G/G we arrive at the conclusion that the phase space of the N-fold product of the topological coset G/G on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of Chern–Simons theory on a Riemann surface of the genus N-1 times the time-line with four Wilson lines.

scholarly journals CANONICAL QUANTIZATION OF THE WZW MODEL WITH DEFECTS AND CHERN–SIMONS THEORY

2010 ◽  
Vol 25 (07) ◽  
pp. 1367-1388 ◽  
Author(s):  
GOR SARKISSIAN
Keyword(s):  
Phase Space ◽  
Boundary Conditions ◽  
Canonical Quantization ◽  
Simons Theory ◽  
Chern Simons ◽  
Chern Simons Theory

We perform canonical quantization of the WZW model with defects and permutation branes. We establish symplectomorphism between phase space of WZW model with N defects on cylinder and phase space of Chern–Simons theory on annulus times R with N Wilson lines, and between phase space of WZW model with N defects on strip and Chern–Simons theory on disk times R with N + 2 Wilson lines. We obtained also symplectomorphism between phase space of the N-fold product of the WZW model on strip with boundary conditions specified by permutation branes, and phase space of Chern–Simons theory on sphere times R with N holes and two Wilson lines.

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.

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

Explicit symplectic-like integration with corrected map for inseparable Hamiltonian

2020 ◽  
Vol 501 (1) ◽  
pp. 1511-1519
Author(s):  
Junjie Luo ◽  
Weipeng Lin ◽  
Lili Yang
Keyword(s):  
Phase Space ◽  
Space Structure ◽  
Eighth Order ◽  
Time Step ◽  
Extended Phase ◽  
Energy Error ◽  
Phase Space Structure ◽  
Compact Binary ◽  
Three Body

ABSTRACT Symplectic algorithms are widely used for long-term integration of astrophysical problems. However, this technique can only be easily constructed for separable Hamiltonian, as preserving the phase-space structure. Recently, for inseparable Hamiltonian, the fourth-order extended phase-space explicit symplectic-like methods have been developed by using the Yoshida’s triple product with a mid-point map, where the algorithm is more effective, stable and also more accurate, compared with the sequent permutations of momenta and position coordinates, especially for some chaotic case. However, it has been found that, for the cases such as with chaotic orbits of spinning compact binary or circular restricted three-body system, it may cause secular drift in energy error and even more the computation break down. To solve this problem, we have made further improvement on the mid-point map with a momentum-scaling correction, which turns out to behave more stably in long-term evolution and have smaller energy error than previous methods. In particular, it could obtain a comparable phase-space distance as computing from the eighth-order Runge–Kutta method with the same time-step.

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.

Infrared finiteness of the two-loop correction to the Chern–Simons term in the Yang–Mills–Chern–Simons theory

1995 ◽  
Vol 73 (5-6) ◽  
pp. 344-348 ◽  
Author(s):  
Yeong-Chuan Kao ◽  
Hsiang-Nan Li
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Landau Gauge ◽  
Quantum Corrections ◽  
Simons Theory ◽  
Loop Correction ◽  
Loop Contribution ◽  
Yang Mills ◽  
Chern Simons ◽  
Chern Simons Theory

We show that the two-loop contribution to the coefficient of the Chern–Simons term in the effective action of the Yang–Mills–Chern–Simons theory is infrared finite in the background field Landau gauge. We also discuss the difficulties in verifying the conjecture, due to topological considerations, that there are no more quantum corrections to the Chern–Simons term other than the well-known one-loop shift of the coefficient.

Is there a phase transition in Maxwell-Chern-Simons theory?

1993 ◽  
Vol 48 (4) ◽  
pp. 1808-1820 ◽  
Author(s):  
Mark Burgess ◽  
David J. Toms ◽  
Nils Tveten
Keyword(s):  
Phase Transition ◽  
Simons Theory ◽  
Chern Simons ◽  
Chern Simons Theory
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