RENORMALIZATION AMBIGUITIES AND GAUGE SYMMETRY IN CHERN–SIMONS THEORIES

1998 ◽  
Vol 13 (07) ◽  
pp. 511-525
Author(s):  
J. L. LÓPEZ
Keyword(s):  
Effective Action ◽  
Three Dimensional ◽  
Gauge Coupling ◽  
Simons Theory ◽  
Radiative Corrections ◽  
Dirac Fermions ◽  
Coupling Constant ◽  
Effective Constant ◽  
Chern Simons ◽  
Chern Simons Theory

The universality of radiative corrections to the gauge coupling constant k of the Chern–Simons theory is studied in a very general regularization scheme in the background gauge formalism. The effective constant k eff induced by radiative corrections can be any real number depending on the balance between the ultraviolet behavior of scalar and pseudoscalar terms in the regularized action. This ambiguity of the effective action is related to the ambiguity in the parity anomaly of three-dimensional Dirac fermions. The effective action also contains a non-analytic term in the gauge field with the same coefficient and opposite gauge transformation in such a way that the effective action is gauge-invariant. The results open the possibility of a connection with non-rational two-dimensional conformal theories for non-integer values of k eff .

PARITY ANOMALY IN CHERN-SIMONS THEORY

1991 ◽  
Vol 06 (08) ◽  
pp. 727-738 ◽  
Author(s):  
G.P. KORCHEMSKY
Keyword(s):  
Gauge Theory ◽  
Effective Action ◽  
Simons Theory ◽  
Coupling Constant ◽  
Classical Action ◽  
Gauge Invariant ◽  
Chern Simons ◽  
Invariant Regularization ◽  
Chern Simons Theory

Ultraviolet (uv) divergences are canceled in the effective action of the D=3 Chern-Simons (CS) gauge theory but regularization is needed. It is impossible to introduce gauge invariant regularization and conserve the parity of the classical action. As a result, in the limit when regularization is removed the finite contribution to the effective action induced by parity-violating regulators remains which being added to the classical action leads to additive integer-valued renormalization of the coupling constant.

Infrared finiteness of the two-loop correction to the Chern–Simons term in the Yang–Mills–Chern–Simons theory

1995 ◽  
Vol 73 (5-6) ◽  
pp. 344-348 ◽  
Author(s):  
Yeong-Chuan Kao ◽  
Hsiang-Nan Li
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Landau Gauge ◽  
Quantum Corrections ◽  
Simons Theory ◽  
Loop Correction ◽  
Loop Contribution ◽  
Yang Mills ◽  
Chern Simons ◽  
Chern Simons Theory

We show that the two-loop contribution to the coefficient of the Chern–Simons term in the effective action of the Yang–Mills–Chern–Simons theory is infrared finite in the background field Landau gauge. We also discuss the difficulties in verifying the conjecture, due to topological considerations, that there are no more quantum corrections to the Chern–Simons term other than the well-known one-loop shift of the coefficient.

scholarly journals CONSISTENT INTERACTIONS IN A THREE-DIMENSIONAL THEORY WITH TENSOR GAUGE FIELDS OF DEGREES TWO AND THREE

2003 ◽  
Vol 18 (24) ◽  
pp. 4451-4468 ◽  
Author(s):  
SOLANGE-ODILE SALIU
Keyword(s):  
Three Dimensional ◽  
Simons Theory ◽  
Gauge Fields ◽  
Dimensional Theory ◽  
Gauge Symmetries ◽  
Lagrangian Action ◽  
Brst Cohomology ◽  
The Relationship ◽  
Chern Simons ◽  
Chern Simons Theory

All consistent interactions in a three-dimensional theory with tensor gauge fields of degrees two and three are obtained by means of the deformation of the solution to the master equation combined with cohomological techniques. The local BRST cohomology of this model allows the deformation of the Lagrangian action, accompanying gauge symmetries and gauge algebra. The relationship with the Chern–Simons theory is discussed.

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 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.

COHERENT STATE QUANTIZATION OF CHERN-SIMONS THEORY

1990 ◽  
Vol 05 (05) ◽  
pp. 959-988 ◽  
Author(s):  
MICHIEL BOS ◽  
V.P. NAIR
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Coherent State ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Three-dimensional Chern-Simons gauge theories are quantized in a functional coherent state formalism. The connection with two-dimensional conformal field theory is found to emerge naturally. The normalized wave functionals are identified as generating functionals for the chiral blocks of two-dimensional current algebra.

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 4d Chern-Simons theory as a 3d Toda theory, and a 3d-2d correspondence

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Meer Ashwinkumar ◽  
Kee-Seng Png ◽  
Meng-Chwan Tan
Keyword(s):  
Moduli Space ◽  
Sigma Model ◽  
Three Dimensional ◽  
Simons Theory ◽  
Yang Mills ◽  
Pole Type ◽  
Type Boundary ◽  
Chern Simons ◽  
Manifold With Corners ◽  
Chern Simons Theory

Abstract We show that the four-dimensional Chern-Simons theory studied by Costello, Witten and Yamazaki, is, with Nahm pole-type boundary conditions, dual to a boundary theory that is a three-dimensional analogue of Toda theory with a novel 3d W-algebra symmetry. By embedding four-dimensional Chern-Simons theory in a partial twist of the five-dimensional maximally supersymmetric Yang-Mills theory on a manifold with corners, we argue that this three-dimensional Toda theory is dual to a two-dimensional topological sigma model with A-branes on the moduli space of solutions to the Bogomolny equations. This furnishes a novel 3d-2d correspondence, which, among other mathematical implications, also reveals that modules of the 3d W-algebra are modules for the quantized algebra of certain holomorphic functions on the Bogomolny moduli space.

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