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.

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 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.

scholarly journals Duality and self-duality of the spin-1 model in the covariant operator formalism

2019 ◽  
Vol 2019 (8) ◽  
Author(s):  
G B de Gracia ◽  
B M Pimentel ◽  
L Rabanal
Keyword(s):  
Hilbert Space ◽  
Vector Field ◽  
Simons Theory ◽  
Indefinite Metric ◽  
Point Function ◽  
Operator Formalism ◽  
Self Duality ◽  
Covariant Operator ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We perform the covariant operator quantization of the spin-$1$ model in $2+1$ spacetime dimensions to rigorously establish its dualities. For this purpose, the Kugo–Ojima–Nakanishi formalism, based on an indefinite metric Hilbert space in the Heisenberg picture, is used. We show that it is possible to extract a massive physical excitation constructed from a linear combination of the vector field $A_{\mu}$ and the $B$-field. In turn, we also show that this excitation generates the Maxwell–Chern–Simons theory. This is achieved by exploring the two-point function of the vector field.

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.

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 .

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.

Sign in / Sign up

Export Citation Format

Share Document