scholarly journals On higher holonomy invariants in higher gauge theory II

2016 ◽  
Vol 13 (07) ◽  
pp. 1650091 ◽  
Author(s):  
Roberto Zucchini
Keyword(s):  
Gauge Theory ◽  
Yield Surface ◽  
Simons Theory ◽  
Crossed Module ◽  
Knot Invariants ◽  
Crossed Modules ◽  
Higher Gauge Theory ◽  
Definition Of ◽  
Chern Simons ◽  
Chern Simons Theory

This is the second of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern–Simons theory. We provide a definition of trace over a crossed module to yield surface knot invariants upon application to 2-holonomies. We show further that the properties of the trace are best described using the theory quandle crossed modules.

scholarly journals On higher holonomy invariants in higher gauge theory I

2016 ◽  
Vol 13 (07) ◽  
pp. 1650090 ◽  
Author(s):  
Roberto Zucchini
Keyword(s):  
Gauge Theory ◽  
Gauge Transformation ◽  
Simons Theory ◽  
Arbitrary Genus ◽  
Higher Gauge Theory ◽  
Chern Simons ◽  
Base Data ◽  
Chern Simons Theory

This is the first of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern–Simons theory. For a flat 2-connection, we define the 2-holonomy of surface knots of arbitrary genus and determine its covariance properties under 1-gauge transformation and change of base data.

scholarly journals STATIC POTENTIAL AND A NEW GENERALIZED CONNECTION IN THREE DIMENSIONS

2004 ◽  
Vol 19 (22) ◽  
pp. 1695-1700 ◽  
Author(s):  
PATRICIO GAETE
Keyword(s):  
Gauge Theory ◽  
Three Dimensions ◽  
Simons Theory ◽  
Static Potential ◽  
Gauge Invariant ◽  
Confining Potential ◽  
Static Interaction ◽  
Pure Gauge Theory ◽  
Chern Simons ◽  
Chern Simons Theory

For a recently proposed pure gauge theory in three dimensions, without a Chern–Simons term, we calculate the static interaction potential within the structure of the gauge-invariant variables formalism. As a consequence, a confining potential is obtained. This result displays a marked qualitative departure from the usual Maxwell–Chern–Simons theory.

A three-dimensional gauge theory

1992 ◽  
Vol 70 (5) ◽  
pp. 301-304 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Gauge Theory ◽  
Scalar Field ◽  
Three Dimensional ◽  
Background Field ◽  
Field Method ◽  
Simons Theory ◽  
Point Function ◽  
Background Field Method ◽  
Chern Simons ◽  
Chern Simons Theory

We investigate a three-dimensional gauge theory modeled on Chern–Simons theory. The Lagrangian is most compactly written in terms of a two-index tensor that can be decomposed into fields with spins zero, one, and two. These all mix under the gauge transformation. The background-field method of quantization is used in conjunction with operator regularization to compute the real part of the two-point function for the scalar field.

scholarly journals THE STRUCTURE OF ADS BLACK HOLES AND CHERN–SIMONS THEORY IN 2 + 1 DIMENSIONS

1999 ◽  
Vol 14 (04) ◽  
pp. 505-520 ◽  
Author(s):  
SHARMANTHIE FERNANDO ◽  
FREYDOON MANSOURI
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gauge Theory ◽  
Excited States ◽  
Simons Theory ◽  
De Sitter ◽  
Sitter Group ◽  
Ads Black Holes ◽  
Chern Simons ◽  
Chern Simons Theory

We study anti-de Sitter black holes in 2 + 1 dimensions in terms of Chern–Simons gauge theory of the anti-de Sitter group coupled to a source. Taking the source to be an anti-de Sitter state specified by its Casimir invariants, we show how all the relevant features of the black hole are accounted for. The requirement that the source be a unitary representation leads to a discrete tower of excited states which provide a microscopic model for the black hole.

scholarly journals PERTURBATIVE CHERN-SIMONS THEORY

1995 ◽  
Vol 04 (04) ◽  
pp. 503-547 ◽  
Author(s):  
DROR BAR-NATAN
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Integral Formula ◽  
Simons Theory ◽  
Gauge Field Theory ◽  
Complete Agreement ◽  
Knot Invariants ◽  
Arf Invariant ◽  
Chern Simons ◽  
Chern Simons Theory

We present the perturbation theory of the Chern-Simons gauge field theory and prove that to second order it indeed gives knot invariants. We identify these invariants and show that in fact we get a previously unknown integral formula for the Arf invariant of a knot, in complete agreement with earlier non-perturbative results of Witten. We outline our expectations for the behavior of the theory beyond two loops.

scholarly journals The Resurgent Structure of Quantum Knot Invariants

2021 ◽  
Author(s):  
Stavros Garoufalidis ◽  
Jie Gu ◽  
Marcos Mariño
Keyword(s):  
Asymptotic Expansion ◽  
Fundamental Solutions ◽  
Simons Theory ◽  
Knot Invariants ◽  
Integer Coefficients ◽  
Bps States ◽  
Formal Power ◽  
Chern Simons ◽  
Resurgent Functions ◽  
Chern Simons Theory

AbstractThe asymptotic expansion of quantum knot invariants in complex Chern–Simons theory gives rise to factorially divergent formal power series. We conjecture that these series are resurgent functions whose Stokes automorphism is given by a pair of matrices of q-series with integer coefficients, which are determined explicitly by the fundamental solutions of a pair of linear q-difference equations. We further conjecture that for a hyperbolic knot, a distinguished entry of those matrices equals to the Dimofte–Gaiotto–Gukov 3D-index, and thus is given by a counting of BPS states. We illustrate our conjectures explicitly by matching theoretically and numerically computed integers for the cases of the $$4_1$$ 4 1 and the $$5_2$$ 5 2 knots.

scholarly journals THE R→α′/R SPACE-TIME DUALITY FROM THE 2+1 POINT OF VIEW

1991 ◽  
Vol 06 (06) ◽  
pp. 501-515 ◽  
Author(s):  
YAN I. KOGAN
Keyword(s):  
Gauge Theory ◽  
Gauge Invariance ◽  
Mass Term ◽  
Point Of View ◽  
Spontaneous Breaking ◽  
Simons Theory ◽  
Membrane Theory ◽  
Small Scales ◽  
Chern Simons ◽  
Chern Simons Theory

The duality between the large and small compactification radii in string theory (bosonic) is considered in the open topological membrane theory. The 2+1 analog of this R→α′/R duality is the duality between large and small scales in the corresponding topologically massive gauge theory with the spontaneous breaking of gauge invariance. This 2+1 duality is a consequence of the equivalence between the Chern-Simons theory with the mass term and the topologically massive gauge theory.

Knot invariants and universal R-matrices from perturbative Chern-Simons theory in the almost axial gauge

1992 ◽  
Vol 379 (1-2) ◽  
pp. 172-198 ◽  
Author(s):  
J.F.W.H. van de Wetering
Keyword(s):  
Simons Theory ◽  
Knot Invariants ◽  
Axial Gauge ◽  
Chern Simons ◽  
Chern Simons Theory

Chern-Simons theory and knot invariants

2016 ◽  
pp. 1-21
Author(s):  
Ramadevi Pichai ◽  
Vivek Singh
Keyword(s):  
Simons Theory ◽  
Knot Invariants ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals DERIVATION OF THE TOTAL TWIST FROM CHERN-SIMONS THEORY

1996 ◽  
Vol 05 (04) ◽  
pp. 489-515 ◽  
Author(s):  
ALLEN C. HIRSHFELD ◽  
UWE SASSENBERG
Keyword(s):  
Three Dimensional ◽  
Simons Theory ◽  
Conway Polynomial ◽  
Knot Invariant ◽  
Euclidian Space ◽  
Original Definition ◽  
Definition Of ◽  
Knot Diagrams ◽  
Chern Simons ◽  
Chern Simons Theory

The total twist number, which represents on one hand the second coefficient of the Alexander-Conway polynomial and on the other hand the first non-trivial Vassiliev knot invariant, is derived from the second order expression of the Wilson loop expectation value in the Chern-Simons theory. Using the well-known fact that the analytical expression is an invariant, a combinatorial expression for the total twist based on the evaluation of knot diagrams is constructed by an appropriate deformation of the knot line in the three-dimensional Euclidian space. The relation to the original definition of the total twist is elucidated.

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