scholarly journals Mimetic discretization of the Abelian Chern-Simons theory and link invariants

2013 ◽  
Vol 54 (12) ◽  
pp. 122302
Author(s):  
Cayetano Di Bartolo ◽  
Javier Grau ◽  
Lorenzo Leal
Keyword(s):  
Simons Theory ◽  
Link Invariants ◽  
Mimetic Discretization ◽  
Chern Simons ◽  
Chern Simons Theory

ABOUT THE UNIQUENESS OF THE KONTSEVICH INTEGRAL

2002 ◽  
Vol 11 (05) ◽  
pp. 759-780 ◽  
Author(s):  
CHRISTINE LESCOP
Keyword(s):  
Uniqueness Theorem ◽  
Simons Theory ◽  
Link Invariants ◽  
Anomaly Formula ◽  
The Relationship ◽  
Chern Simons ◽  
Chern Simons Theory

We refine a Le and Murakami uniqueness theorem for the Kontsevich Integral in order to specify the relationship between the two (possibly equal) main universal Vassiliev link invariants: the Kontsevich Integral and the perturbative expression of the Chern-Simons theory. As a corollary, we prove that the Altschuler and Freidel anomaly [Formula: see text]-that groups the Bott and Taubes anomalous terms- is a combination of diagrams with two univalent vertices and we explicitly define the isomorphism of [Formula: see text] which transforms the Kontsevich integral into the Poirier limit of the perturbative expression of the Chern-Simons theory for framed links, as a function of α

scholarly journals Wilson lines in Chern-Simons theory and link invariants

1990 ◽  
Vol 330 (2-3) ◽  
pp. 575-607 ◽  
Author(s):  
E. Guadagnini ◽  
M. Martellini ◽  
M. Mintchev
Keyword(s):  
Simons Theory ◽  
Link Invariants ◽  
Chern Simons ◽  
Chern Simons Theory

CHERN-SIMONS THEORY AND KAUFFMAN POLYNOMIALS

1990 ◽  
Vol 05 (06) ◽  
pp. 1165-1195 ◽  
Author(s):  
YONG-SHI WU ◽  
KENGO YAMAGISHI
Keyword(s):  
Lie Algebras ◽  
Simons Theory ◽  
Wilson Loops ◽  
Expectation Values ◽  
Simple Lie Algebras ◽  
Link Invariants ◽  
Chern Simons ◽  
Knots And Links ◽  
Chern Simons Theory

We report on a study of the expectation values of Wilson loops in D=3 Chern-Simons theory. The general skein relations (of higher orders) are derived for these expectation values. We show that the skein relations for the Wilson loops carrying the fundamental representations of the simple Lie algebras SO(n) and Sp(n) are sufficient to determine invariants for all knots and links and that the resulting link invariants agree with Kauffman polynomials. The polynomial for an unknotted circle is identified to the formal characters of the fundamental representations of these Lie algebras.

scholarly journals Topologically massive Yang–Mills theory and link invariants

2015 ◽  
Vol 30 (07) ◽  
pp. 1550034 ◽  
Author(s):  
Tuna Yildirim
Keyword(s):  
Geometric Quantization ◽  
Simons Theory ◽  
Small Contribution ◽  
Topological Theory ◽  
Yang Mills ◽  
Link Invariants ◽  
Mass Gap ◽  
Level Number ◽  
Chern Simons ◽  
Chern Simons Theory

Topologically massive Yang–Mills theory is studied in the framework of geometric quantization. Since this theory has a mass gap proportional to the topological mass m, Yang–Mills contribution decays exponentially at very large distances compared to 1/m, leaving a pure Chern–Simons theory with level number k. In this paper, the near Chern–Simons limit is studied where the distance is large enough to give an almost topological theory, with a small contribution from the Yang–Mills term. It is shown that this almost topological theory consists of two copies of Chern–Simons with level number k/2, very similar to the Chern–Simons splitting of topologically massive AdS gravity. Also, gauge invariance of these half-Chern–Simons theories is discussed. As m approaches to infinity, the split parts add up to give the original Chern–Simons term with level k. Reduction of the phase space is discussed in this limit. Finally, a relation between the observables of topologically massive Yang–Mills theory and Chern–Simons theory is shown. One of the two split Chern–Simons pieces is shown to be associated with Wilson loops while the other with 't Hooft loops. This allows one to use skein relations to calculate topologically massive Yang–Mills theory observables in the near Chern–Simons limit.

scholarly journals DUALITY IN osp(1|2) CONFORMAL FIELD THEORY AND LINK INVARIANTS

1998 ◽  
Vol 13 (17) ◽  
pp. 2931-2978 ◽  
Author(s):  
I. P. ENNES ◽  
A. V. RAMALLO ◽  
J. M. SANCHEZ DE SANTOS ◽  
P. RAMADEVI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Simons Theory ◽  
Conformal Blocks ◽  
Link Invariants ◽  
Conformal Field ◽  
Free Field Realization ◽  
Chern Simons ◽  
Knots And Links ◽  
Chern Simons Theory

We study the crossing symmetry of the conformal blocks of the conformal field theory based on the affine Lie superalgebra osp(1|2). Within the framework of a free field realization of the osp(1|2) current algebra, the fusion and braiding matrices of the model are determined. These results are related in a simple way to those corresponding to the su(2) algebra by means of a suitable identification of parameters. In order to obtain the link invariants corresponding to the osp(1|2) conformal field theory, we analyze the corresponding topological Chern–Simons theory. In a first approach we quantize the Chern–Simons theory on the torus and, as a result, we get the action of the Wilson line operators on the supercharacters of the affine osp(1|2). From this result we get a simple expression relating the osp(1|2) polynomials for torus knots and links to those corresponding to the su(2) algebra. Further, this relation is verified for arbitrary knots and links by quantizing the Chern–Simons theory on the punctured two-sphere.

scholarly journals Topological gauge fixing II: A homotopy formulation

2015 ◽  
Vol 30 (20) ◽  
pp. 1550102 ◽  
Author(s):  
L. Gallot ◽  
E. Pilon ◽  
F. Thuillier
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Simons Theory ◽  
Homotopy Operator ◽  
Link Invariants ◽  
Gauge Fixing ◽  
Chern Simons ◽  
Chern Simons Theory

We revisit the implementation of the metric-independent Fock–Schwinger gauge in the Abelian Chern–Simons field theory defined in ℝ3 by means of a homotopy condition. This leads to the Lagrangian [Formula: see text] in terms of curvatures F and of the Poincaré homotopy operator h. The corresponding field theory provides the same link invariants as the Abelian Chern–Simons theory. Incidentally the part of the gauge field propagator which yields the link invariants of the Chern–Simons theory in the Fock–Schwinger gauge is recovered without any computation.

KNOTS IN THE NON-ABELIAN CHERN–SIMONS THEORY

2004 ◽  
Vol 19 (35) ◽  
pp. 2629-2636
Author(s):  
PENG-MING ZHANG ◽  
YI-SHI DUAN ◽  
XIN LIU
Keyword(s):  
Simons Theory ◽  
Link Invariants ◽  
Chern Simons ◽  
Mapping Theory ◽  
Chern Simons Theory

We employ a spinor decomposition of SU (2) connection to study the Chern–Simons form. Our results show that the SU (2) Chern–Simons action yields the link invariants. Then the structure of the knots is discussed with the ϕ-mapping theory.

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