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.

scholarly journals Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory

2002 ◽  
Vol 2002 (01) ◽  
pp. 002-002 ◽  
Author(s):  
Alexander Gorsky ◽  
Ian I Kogan ◽  
Chris Korthals-Altes
Keyword(s):  
Quantum Hall ◽  
Simons Theory ◽  
Quantum Hall System ◽  
Chern Simons ◽  
Chern Simons Theory

FLUID DYNAMICS, CHERN-SIMONS THEORY, AND THE QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (16n17) ◽  
pp. 2735-2749 ◽  
Author(s):  
SAFI BAHCALL ◽  
LEONARD SUSSKIND
Keyword(s):  
Magnetic Field ◽  
Fluid Dynamics ◽  
Gauge Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Simons Theory ◽  
Quantum Hall System ◽  
Chern Simons ◽  
Chern Simons Theory

In this paper we show that classical fluid dynamics in a plane is a gauge theory useful for studying aspects of the quantum Hall system. When the fluid is charged and placed in a magnetic field, Chern-Simons fields appear naturally and the fractional statistics of vortex excitations can be understood qualitatively. Applying the fluid picture to a gas of anyons shows that it superconducts.

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.

scholarly journals AREA-PRESERVING DIFFEOMORPHISMS, W∞ AND ${\mathcal U}_q [{\rm sl}(2)]$ IN CHERN–SIMONS THEORY AND THE QUANTUM HALL SYSTEM

1994 ◽  
Vol 09 (21) ◽  
pp. 3887-3911 ◽  
Author(s):  
IAN I. KOGAN
Keyword(s):  
Gauge Theory ◽  
Quantum Hall ◽  
Simons Theory ◽  
Two Dimensional ◽  
Canonical Transformations ◽  
Dimensional Phase Space ◽  
Quantum Hall System ◽  
Chern Simons ◽  
Area Preserving ◽  
Chern Simons Theory

We discuss a quantum [Formula: see text] symmetry in the Landau problem, which naturally arises due to the relation between [Formula: see text] and the group of magnetic translations. The latter is connected with W∞ and area-preserving (symplectic) diffeomorphisms which are the canonical transformations in the two-dimensional phase space. We shall discuss the hidden quantum symmetry in a 2 + 1 gauge theory with the Chern–Simons term and in a quantum Hall system, which are both connected with the Landau problem.

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.

scholarly journals BATALIN–VILKOVISKY YANG–MILLS THEORY AS A HOMOTOPY CHERN–SIMONS THEORY VIA STRING FIELD THEORY

2009 ◽  
Vol 24 (07) ◽  
pp. 1309-1331 ◽  
Author(s):  
ANTON M. ZEITLIN
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Simons Theory ◽  
Yang Mills ◽  
Algebraic Constructions ◽  
Chern Simons ◽  
Chern Simons Theory

We show explicitly how Batalin–Vilkovisky Yang–Mills action emerges as a homotopy generalization of Chern–Simons theory from the algebraic constructions arising from string field theory.

scholarly journals $$ T\overline{T} $$-deformation of q-Yang-Mills theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Leonardo Santilli ◽  
Richard J. Szabo ◽  
Miguel Tierz
Keyword(s):  
Phase Transition ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Line Bundles ◽  
Boltzmann Entropy ◽  
Third Order ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We derive the $$ T\overline{T} $$ T T ¯ -perturbed version of two-dimensional q-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the $$ T\overline{T} $$ T T ¯ -deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large N factorization into chiral and anti-chiral sectors. For the U(N) gauge theory on the sphere, we show that the large N phase transition persists, and that it is of third order and induced by instantons. The effect of the $$ T\overline{T} $$ T T ¯ -deformation is to decrease the critical value of the ’t Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for (q, t)-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large N limit of Yang-Mills theory, showing that the $$ T\overline{T} $$ T T ¯ -deformation decreases the contribution of the Boltzmann entropy.

scholarly journals HIERARCHICAL WAVE FUNCTIONS OF FRACTIONAL QUANTUM HALL EFFECT ON THE TORUS

1993 ◽  
Vol 07 (14) ◽  
pp. 2655-2665 ◽  
Author(s):  
DINGPING LI
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Wave Functions ◽  
Simons Theory ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Chern Simons ◽  
Chern Simons Theory

One kind of hierarchical wave functions of Fractional Quantum Hall Effect on the torus is constructed. We find that the wave functions are closely related to the wave functions of generalized Abelian Chern-Simons theory.

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