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.

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.

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 NEW GAUGE INVARIANT FORMULATION OF THE CHERN–SIMONS GAUGE THEORY: CLASSICAL AND QUANTAL ANALYSIS

2009 ◽  
Vol 24 (31) ◽  
pp. 5933-5975
Author(s):  
MU-IN PARK ◽  
YOUNG-JAI PARK
Keyword(s):  
Gauge Theory ◽  
Longitudinal Mode ◽  
Momentum Tensor ◽  
Simons Theory ◽  
Gauge Invariant ◽  
Invariant Formulation ◽  
Poincaré Algebra ◽  
Chern Simons ◽  
Schrödinger Picture ◽  
Chern Simons Theory

A recently proposed new gauge invariant formulation of the Chern–Simons gauge theory is considered in detail. This formulation is consistent with the gauge fixed formulation. Furthermore, it is found that the canonical (Noether) Poincaré generators are not gauge invariant even on the constraints surface and do not satisfy the Poincaré algebra contrast to usual case. It is the improved generators, constructed from the symmetric energy–momentum tensor, which are (manifestly) gauge invariant and obey the quantum as well as classical Poincaré algebra. The physical states are constructed and it is found in the Schrödinger picture that unusual gauge invariant longitudinal mode of the gauge field is crucial for constructing the physical wave-functional which is genuine to (pure) Chern–Simons theory. In matching to the gauge fixed formulation, we consider three typical gauges, Coulomb, axial and Weyl gauges as explicit examples. Furthermore, recent several confusions about the effect of Dirac's dressing function and the gauge fixings are clarified. The analysis according to old gauge independent formulation á la Dirac is summarized in an appendix.

scholarly journals NOETHER CONSERVATION LAWS IN HIGHER-DIMENSIONAL CHERN–SIMONS THEORY

2003 ◽  
Vol 18 (37) ◽  
pp. 2645-2651 ◽  
Author(s):  
GIOVANNI GIACHETTA ◽  
LUIGI MANGIAROTTI ◽  
GENNADI SARDANASHVILY
Keyword(s):  
Gauge Theory ◽  
Conservation Laws ◽  
Conservation Law ◽  
Simons Theory ◽  
Gauge Invariant ◽  
Higher Dimensional ◽  
Chern Simons ◽  
Noether Current ◽  
Chern Simons Theory

Though a global Chern–Simons (2k-1)-form is not gauge-invariant, this form seen as a Lagrangian of higher-dimensional gauge theory leads to the conservation law of a modified Noether current.

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 Explicit Connection Between Conformal Field Theory and 2+1 Chern–Simons Theory

1997 ◽  
Vol 12 (23) ◽  
pp. 1687-1697
Author(s):  
Daniel C. Cabra ◽  
Gerardo L. Rossini
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Wilson Loop ◽  
Simons Theory ◽  
Gauge Invariant ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

We give explicit field theoretical representations for the observables of (2+1)-dimensional Chern–Simons theory in terms of gauge-invariant composites of 2-D WZW fields. To test our identification we compute some basic Wilson loop correlators and re-obtain the known results.

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 Yang-Mills theory, 2 + 1 and 3 + 1 dimensions

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2415-2422 ◽  
Author(s):  
V. P. NAIR
Keyword(s):  
String Tension ◽  
Simons Theory ◽  
Nonzero Temperature ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Magnetic Mass ◽  
Chern Simons ◽  
Chern Simons Theory

I review the analysis of (2+1)-dimensional Yang-Mills (YM2+1) theory via the use of gauge-invariant matrix variables. The vacuum wavefunction, string tension, the propagator mass for gluons, its relation to the magnetic mass for YM3+1at nonzero temperature and the extension of our analysis to the Yang-Mills-Chern-Simons theory are discussed. A possible extension to 3 + 1 dimensions is also briefly considered.

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