CHERN–SIMONS THEORY, HIDA DISTRIBUTIONS, AND STATE MODELS

2003 ◽  
Vol 06 (supp01) ◽  
pp. 65-81 ◽  
Author(s):  
S. ALBEVERIO ◽  
A. HAHN ◽  
A. N. SENGUPTA
Keyword(s):  
Wilson Loop ◽  
Functional Integral ◽  
Simons Theory ◽  
Infinite Dimensional ◽  
Linking Number ◽  
Gauge Fixing ◽  
Regularization Techniques ◽  
State Models ◽  
Chern Simons ◽  
Chern Simons Theory

In this paper we present the central ideas and results of a rigorous theory of the Chern–Simons functional integral. In particular, we show that it is possible to define the Wilson loop observables (WLOs) for pure Chern–Simons models with base manifold M = ℝ3 rigorously as infinite dimensional oscillatory integrals by exploiting an "axial gauge fixing" and applying certain regularization techniques like "loop-smearing" and "framing". The (values of the) WLOs can be computed explicitly. If the structure group G of the model is Abelian one obtains well-known linking number expressions for the WLOs. If G is Non-Abelian one obtains expressions which are similar but not identical to the state model representations for the Homfly and Kauffman polynomials given in [19, 21, 31].

scholarly journals Geometric aspects of interpolating gauge-fixing in Chern–Simons theory

2018 ◽  
Vol 33 (02) ◽  
pp. 1850012
Author(s):  
Laurent Gallot ◽  
Philippe Mathieu ◽  
Éric Pilon ◽  
Frank Thuillier
Keyword(s):  
Simons Theory ◽  
3 Dimensional ◽  
Linking Number ◽  
Gauge Fixing ◽  
Covariant Gauge ◽  
Chern Simons ◽  
Chern Simons Theory

In this paper we investigate an interpolating gauge-fixing procedure in (4l + 3)-dimensional Abelian Chern–Simons theory. We show that this interpolating gauge is related to the covariant gauge in a constant anisotropic metric. We compute the corresponding propagators involved in various expressions of the linking number in various gauges. We comment on the geometric interpretations of these expressions, clarifying how to pass from one interpretation to another.

scholarly journals Explicit Connection Between Conformal Field Theory and 2+1 Chern–Simons Theory

1997 ◽  
Vol 12 (23) ◽  
pp. 1687-1697
Author(s):  
Daniel C. Cabra ◽  
Gerardo L. Rossini
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Wilson Loop ◽  
Simons Theory ◽  
Gauge Invariant ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

We give explicit field theoretical representations for the observables of (2+1)-dimensional Chern–Simons theory in terms of gauge-invariant composites of 2-D WZW fields. To test our identification we compute some basic Wilson loop correlators and re-obtain the known results.

A THREE-DIMENSIONAL COVARIANT APPROACH TO MONODROMY (SKEIN RELATIONS) IN CHERN-SIMONS THEORY

1990 ◽  
Vol 05 (32) ◽  
pp. 2747-2751 ◽  
Author(s):  
B. BRODA
Keyword(s):  
Integral Representation ◽  
Path Integral ◽  
Wilson Loop ◽  
Three Dimensional ◽  
Simons Theory ◽  
Monodromy Operator ◽  
Covariant Approach ◽  
Path Integral Representation ◽  
Chern Simons ◽  
Chern Simons Theory

A genuinely three-dimensional covariant approach to the monodromy operator (skein relations) in the context of Chern-Simons theory is proposed. A holomorphic path-integral representation for the holonomy operator (Wilson loop) and for the non-abelian Stokes theorem is used.

A Combinatorial Link Invariant of Finite Type Derived from Chern-Simons Theory

1997 ◽  
Vol 06 (02) ◽  
pp. 243-280 ◽  
Author(s):  
Allen C. Hirshfeld ◽  
Uwe Sassenberg ◽  
Thomas Klöker
Keyword(s):  
Wilson Loop ◽  
Perturbation Expansion ◽  
Simons Theory ◽  
Link Invariant ◽  
Third Order ◽  
Expectation Value ◽  
Knot Invariant ◽  
Chern Simons ◽  
Combinatorial Expression ◽  
Chern Simons Theory

We derive from the perturbation expansion of the Wilson loop expectation value in the Chern-Simons theory an explicit combinatorial expression for a third-order finite link invariant, thereby generalising the knot invariant considered in a previous article.

scholarly journals 1/2BPS Wilson loop inN=6superconformal Chern-Simons theory at two loops

2013 ◽  
Vol 88 (2) ◽  
Author(s):  
Marco S. Bianchi ◽  
Gaston Giribet ◽  
Matias Leoni ◽  
Silvia Penati
Keyword(s):  
Wilson Loop ◽  
Simons Theory ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals On the Quantization of Isomonodromic Deformations on the Torus

1997 ◽  
Vol 12 (11) ◽  
pp. 2013-2029 ◽  
Author(s):  
D. Korotkin ◽  
H. Samtleben
Keyword(s):  
Poisson Bracket ◽  
Poisson Structure ◽  
Hamiltonian Formulation ◽  
Simons Theory ◽  
Isomonodromic Deformation ◽  
Isomonodromic Deformations ◽  
Gauge Fixing ◽  
Meromorphic Connection ◽  
Chern Simons ◽  
Chern Simons Theory

The quantization of isomonodromic deformation of a meromorphic connection on the torus is shown to lead directly to the Knizhnik–Zamolodchikov–Bernard equations in the same way as the problem on the sphere leads to the system of Knizhnik–Zamolodchikov equations. The Poisson bracket required for a Hamiltonian formulation of isomonodromic deformations is naturally induced by the Poisson structure of Chern–Simons theory in a holomorphic gauge fixing. This turns out to be the origin of the appearance of twisted quantities on the torus.

Hamiltonian, path integral, and BRST formulations of the Chern–Simons theory under appropriate gauge-fixing

2008 ◽  
Vol 86 (2) ◽  
pp. 401-407 ◽  
Author(s):  
U Kulshreshtha ◽  
D S Kulshreshtha
Keyword(s):  
Path Integral ◽  
Hamiltonian Path ◽  
Simons Theory ◽  
Gauge Fixing ◽  
Chern Simons ◽  
Chern Simons Theory

The Hamiltonian, path integral, and BRST formulations of the Chern–Simons theory in two-space one-time dimensions are investigated under appropriate gauge-fixing conditions.PACS Nos.: 11.10.Ef, 11.10.Kk, 12.20.Ds

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.

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