Perturbative expansion of Chern-Simons theory with non-compact gauge group

1991 ◽  
Vol 141 (2) ◽  
pp. 423-440 ◽  
Author(s):  
Dror Bar-Natan ◽  
Edward Witten
Keyword(s):  
Gauge Group ◽  
Perturbative Expansion ◽  
Simons Theory ◽  
Chern Simons ◽  
Compact Gauge Group ◽  
Chern Simons Theory

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.

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

On the phase of Chern-Simons theory with complex gauge group

1995 ◽  
Vol 28 (19) ◽  
pp. 5581-5587
Author(s):  
R Gibbs ◽  
S Mokhtari
Keyword(s):  
Gauge Group ◽  
Simons Theory ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals On resolutions of cosmological singularities in higher-spin gravity

2019 ◽  
Vol 28 (15) ◽  
pp. 1950168
Author(s):  
Benjamin Burrington ◽  
Leopoldo A. Pando Zayas ◽  
Nicholas Rombes
Keyword(s):  
Gauge Group ◽  
Three Dimensional ◽  
Big Bang ◽  
Simons Theory ◽  
Gauge Potential ◽  
Cosmological Singularity ◽  
Gauge Transformations ◽  
Higher Spin ◽  
Chern Simons ◽  
Chern Simons Theory

We study the resolution of certain cosmological singularity in the context of higher-spin three-dimensional gravity. We consider gravity coupled to a spin-3 field realized as Chern–Simons theory with gauge group [Formula: see text]. In this context, we elaborate and extend a singularity resolution scheme proposed by Krishnan and Roy. We discuss the resolution of a big bang singularity in the case of gravity coupled to a spin-4 field realized as Chern–Simons theory with gauge group [Formula: see text]. In all these cases, we show the existence of gauge transformations that do not change the holonomy of the Chern–Simons gauge potential and lead to metrics without the initial singularity. We argue that such transformations always exist in the context of gravity coupled to a spin-[Formula: see text] field when described by Chern–Simons with gauge group [Formula: see text].

scholarly journals Exact results for perturbative Chern–Simons theory with complex gauge group

2009 ◽  
Vol 3 (2) ◽  
pp. 363-443 ◽  
Author(s):  
Tudor Dimofte ◽  
Sergei Gukov ◽  
Jonatan Lenells ◽  
Don Zagier
Keyword(s):  
Gauge Group ◽  
Simons Theory ◽  
Exact Results ◽  
Chern Simons ◽  
Chern Simons Theory

A LATTICE MODEL OF FRACTIONAL STATISTICS

1991 ◽  
Vol 05 (16n17) ◽  
pp. 2701-2733 ◽  
Author(s):  
RONALD KANTOR ◽  
LEONARD SUSSKIND
Keyword(s):  
Gauge Group ◽  
Continuum Limit ◽  
Three Dimensional ◽  
Simons Theory ◽  
Fractional Statistics ◽  
Angular Momenta ◽  
New Formulation ◽  
Chern Simons ◽  
The Continuum ◽  
Chern Simons Theory

We present a new formulation of Chern-Simons theory on a three-dimensional lattice, with either the linear gauge group R or the finite cyclic gauge group Z N. By coupling extended objects called dumb-bells to the lattice Chern-Simons field, we obtain a model exhibiting fractional statistics in the continuum limit. Internal dumb-bell angular momenta take values consistent with their statistics. The Z N-model has a gauge-decoupled condensate. Either model can admit a Maxwell term.

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