ABELIAN CHERN–SIMONS THEORY WITH MATTER FIELDS

1992 ◽  
Vol 07 (02) ◽  
pp. 381-405 ◽  
Author(s):  
KYUNG-HYUN CHO ◽  
CHAIHO RIM
Keyword(s):  
Hilbert Space ◽  
Gauge Field ◽  
Unitary Transformation ◽  
Simons Theory ◽  
Nonlocal Interaction ◽  
Maxwell Theory ◽  
Chern Simons ◽  
Matter Fields ◽  
Chern Simons Theory

It is shown that in the Abelian Chern–Simons plus Maxwell theory in 1 + 2 dimensions there is a unitary transformation such that massless modes of the gauge field are eliminated completely in the Hilbert space and a nonlocal interaction between matter fields (fermions or scalars) remains instead. The nonlocal interaction is given in terms of an effective gauge field satisfying the Gauss constraint. It is also pointed out that it is the nonlocal interaction that changes the statistics of pointlike particles and that makes a vortex charged.

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 Duality and self-duality of the spin-1 model in the covariant operator formalism

2019 ◽  
Vol 2019 (8) ◽  
Author(s):  
G B de Gracia ◽  
B M Pimentel ◽  
L Rabanal
Keyword(s):  
Hilbert Space ◽  
Vector Field ◽  
Simons Theory ◽  
Indefinite Metric ◽  
Point Function ◽  
Operator Formalism ◽  
Self Duality ◽  
Covariant Operator ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We perform the covariant operator quantization of the spin-$1$ model in $2+1$ spacetime dimensions to rigorously establish its dualities. For this purpose, the Kugo–Ojima–Nakanishi formalism, based on an indefinite metric Hilbert space in the Heisenberg picture, is used. We show that it is possible to extract a massive physical excitation constructed from a linear combination of the vector field $A_{\mu}$ and the $B$-field. In turn, we also show that this excitation generates the Maxwell–Chern–Simons theory. This is achieved by exploring the two-point function of the vector field.

scholarly journals Edge States from Defects on the Noncommutative Plane

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2509-2516 ◽  
Author(s):  
A. Pinzul ◽  
A. Stern
Keyword(s):  
Hilbert Space ◽  
Point Defects ◽  
Nonlinear Deformation ◽  
Simons Theory ◽  
Edge States ◽  
Boundary States ◽  
Chern Simons ◽  
Spatial Support ◽  
Noncommutative Plane ◽  
Chern Simons Theory

We illustrate how boundary states are recovered when going from a noncommutative manifold to a commutative one with a boundary. Our example is the noncommutative plane with a defect, whose commutative limit was found to be a punctured plane - so here the boundary is one point. Defects were introduced by removing states from the standard harmonic oscillator Hilbert space. For Chern-Simons theory, the defect acts as a source, which was found to be associated with a nonlinear deformation of the w∞ algebra. The undeformed w∞ algebra is recovered in the commutative limit, and here we show that its spatial support is in a tiny region near the puncture.

scholarly journals Averaging over moduli in deformed WZW models

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Junkai Dong ◽  
Thomas Hartman ◽  
Yikun Jiang
Keyword(s):  
Moduli Space ◽  
Central Charge ◽  
Principal Result ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Chern Simons ◽  
Conserved Currents ◽  
Matter Fields ◽  
Chern Simons Theory

Abstract WZW models live on a moduli space parameterized by current-current deformations. The moduli space defines an ensemble of conformal field theories, which generically have N abelian conserved currents and central charge c > N. We calculate the average partition function and show that it can be interpreted as a sum over 3-manifolds. This suggests that the ensemble-averaged theory has a holographic dual, generalizing recent results on Narain CFTs. The bulk theory, at the perturbative level, is identified as U(1)2N Chern-Simons theory coupled to additional matter fields. From a mathematical perspective, our principal result is a Siegel-Weil formula for the characters of an affine Lie algebra.

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