scholarly journals The Algebra of Chern—Simons Classes, the Poisson Bracket on it, and the Action of the Gauge Group

1994 ◽  
pp. 261-288 ◽  
Author(s):  
Israel M. Gelfand ◽  
Mikhail M. Smirnov
Keyword(s):  
Poisson Bracket ◽  
Gauge Group ◽  
Chern Simons

THE HOMFLY POLYNOMIAL FOR TORUS LINKS FROM CHERN–SIMONS GAUGE THEORY

1995 ◽  
Vol 10 (07) ◽  
pp. 1045-1089 ◽  
Author(s):  
J. M. F. LABASTIDA ◽  
M. MARIÑO
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Homfly Polynomial ◽  
Fundamental Representation ◽  
Torus Knots ◽  
Polynomial Invariants ◽  
Chern Simons ◽  
Knots And Links ◽  
Torus Links

Polynomial invariants corresponding to the fundamental representation of the gauge group SU(N) are computed for arbitrary torus knots and links in the framework of Chern–Simons gauge theory making use of knot operators. As a result, a formula for the HOMFLY polynomial for arbitrary torus links is presented.

scholarly journals GAUGING OF CHERN-SIMONS p-BRANES

1994 ◽  
Vol 09 (19) ◽  
pp. 3367-3375 ◽  
Author(s):  
RAIKO P. ZAIKOV
Keyword(s):  
Phase Space ◽  
Poisson Bracket ◽  
Target Space ◽  
Closed Algebra ◽  
Chern Simons ◽  
Infinite Set

The Chern-Simons membranes and in general the Chern-Simons p-branes moving in D-dimensional target space admit an infinite set of secondary constraints. With respect to the Poisson bracket these constraints form a closed algebra which contains the classical W1+∞ algebra in p dimensions as a subalgebra. A corresponding gauged theory in the phase space is constructed in a Hamiltonian gauge as an analog of the ordinary W gravity.

THE NONABELIAN CHERN-SIMONS TERM WITH SOURCES AND EXOTIC SOURCE STATISTICS

1989 ◽  
Vol 04 (20) ◽  
pp. 1923-1935 ◽  
Author(s):  
A.P. BALACHANDRAN ◽  
M. BOURDEAU ◽  
S. JO
Keyword(s):  
Gauge Group ◽  
Vector Potential ◽  
Field Equations ◽  
All Solutions ◽  
Chern Simons

A system of N identical nonabelian sources interacting with a nonabelian vector potential in 2+1 dimensions is considered. The Lagrangian for the potential is the Chern-Simons term. All solutions of the field equations are constructed. The statistics of the sources is found to exhibit several novel features. In particular, it depends on the potential by which they interact and is not unique. For the gauge group SU(2), among the possible statistics is that of a 1/2 fermion. Self interaction is explicitly shown to generate an intrinsic spin for the nonabelian source just as for the abelian source. Although only the group SU(2) is considered in detail in this paper, most of its results generalize to other groups.

scholarly journals Doubled lattice Chern–Simons–Yang–Mills theories with discrete gauge group

2016 ◽  
Vol 374 ◽  
pp. 255-290 ◽  
Author(s):  
S. Caspar ◽  
D. Mesterházy ◽  
T.Z. Olesen ◽  
N.D. Vlasii ◽  
U.-J. Wiese
Keyword(s):  
Gauge Group ◽  
Yang Mills ◽  
Chern Simons

scholarly journals What Chern–Simons theory assigns to a point

2017 ◽  
Vol 114 (51) ◽  
pp. 13418-13423 ◽  
Author(s):  
André G. Henriques
Keyword(s):  
Gauge Group ◽  
Von Neumann Algebras ◽  
Mathematical Object ◽  
Loop Group ◽  
Simons Theory ◽  
Fusion Product ◽  
Positive Energy ◽  
Von Neumann ◽  
Chern Simons ◽  
Chern Simons Theory

We answer the questions, “What does Chern–Simons theory assign to a point?” and “What kind of mathematical object does Chern–Simons theory assign to a point?” Our answer to the first question is representations of the based loop group. More precisely, we identify a certain class of projective unitary representations of the based loop group 𝛀G. We define the fusion product of such representations, and we prove that, modulo certain conjectures, the Drinfel’d center of that representation category of 𝛀G is equivalent to the category of positive energy representations of the free loop group LG.† The abovementioned conjectures are known to hold when the gauge group is abelian or of type A1. Our answer to the second question is bicommutant categories. The latter are higher categorical analogs of von Neumann algebras: They are tensor categories that are equivalent to their bicommutant inside Bim(R), the category of bimodules over a hyperfinite 𝐼𝐼𝐼1 factor. We prove that, modulo certain conjectures, the category of representations of the based loop group is a bicommutant category. The relevant conjectures are known to hold when the gauge group is abelian or of type An.

scholarly journals On partition functions of refined Chern-Simons theories on S3

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
M.Y. Avetisyan ◽  
R.L. Mkrtchyan
Keyword(s):  
Partition Function ◽  
Gauge Group ◽  
Topological Strings ◽  
Simons Theory ◽  
Partition Functions ◽  
Coupling Constant ◽  
Sine Functions ◽  
Chern Simons ◽  
Arbitrary Gauge ◽  
Chern Simons Theory

Abstract We present a new expression for the partition function of the refined Chern-Simons theory on S3 with an arbitrary gauge group, which is explicitly equal to 1 when the coupling constant is zero. Using this form of the partition function we show that the previously known Krefl-Schwarz representation of the partition function of the refined Chern-Simons theory on S3 can be generalized to all simply laced algebras.For all non-simply laced gauge algebras, we derive similar representations of that partition function, which makes it possible to transform it into a product of multiple sine functions aiming at the further establishment of duality with the refined topological strings.

NON-ABELIAN GAUGE THEORY FOR CHERN–SIMONS PATH INTEGRAL ON R3

2012 ◽  
Vol 21 (04) ◽  
pp. 1250039 ◽  
Author(s):  
ADRIAN P. C. LIM
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Path Integral ◽  
Wilson Loop ◽  
Wiener Measure ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Chern Simons

In a prequel to this article, we used abstract Wiener measure to define the Chern–Simons path integral over ℝ3. In this sequel, we compute the Wilson Loop observable for the non-abelian gauge group and compare with current knot literature.

scholarly journals Subleading corrections to the free energy in a theory with N5/3 scaling

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
James T. Liu ◽  
Yifan Lu
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Gauge Group ◽  
Leading Order ◽  
Numerical Evidence ◽  
Matter Theory ◽  
Chern Simons

Abstract We numerically investigate the sphere partition function of a Chern-Simons-matter theory with SU(N) gauge group at level k coupled to three adjoint chiral multiplets that is dual to massive IIA theory. Beyond the leading order N5/3 behavior of the free energy, we find numerical evidence for a term of the form (2/9) log N. We conjecture that this term may be universal in theories with N5/3 scaling in the large-N limit with the Chern-Simons level k held fixed.

scholarly journals Chern-Simons theory with finite gauge group

1993 ◽  
Vol 156 (3) ◽  
pp. 435-472 ◽  
Author(s):  
Daniel S. Freed ◽  
Frank Quinn
Keyword(s):  
Gauge Group ◽  
Simons Theory ◽  
Chern Simons ◽  
Chern Simons Theory
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