Gauss law constraints in Chern-Simons theory from BRST quantization

Abstract

The physical state condition in the BRST quantization of Chern-Simons field theory is used to derive Gauss law constraints in the presence of Wilson loops, which play an important role in explicitly establishing the connection of Chern-Simons field theory with 2-dimensional conformal field theory.When we discuss knot invariants in terms of Chern-Simons theory [1][2][3][4][5][6] and the relationship between Chern-Simons field theory and conformal field theory [7,8] , an important relation is Gauss law constraint in presence of Wilson line, which was first given in ref.[1].This relation plays an important role in proving that states of Chern-Simons theory satisfy the Knizhnik-Zamolodchikov equation [9][10][11][12][13] . In this letter we intend to derive the Gauss law constraints from BRST quantization of Chern-Simons field theory. We think this investigation is significant since in some sense BRST quantization formulation is defined better than a formal manipulation without gauge fixing [14] . We will show that when Wilson lines exist the physical state condition in BRST quantization will lead to Gauss law constraints † ICSC-World Laboratory, Switzerland

Mtheory on deformed superspace

“…The effect of addition of a bare mass term on the BRST and the anti-BRST symmetries has also been analysed in the non-linear gauges [40]. The BRST symmetry for the Chern-Simons theory has also been thoroughly investigated [35,41]. The BRST symmetry of N = 1 abelian Chern-Simons theory [42] and N = 1 non-abelian Chern-Simons theory [43] has been analysed in the superspace formalism.…”

Gauge and supersymmetric invariance of a boundary Bagger-Lambert-Gustavsson theory

“…This invariance of the theory under BRST symmetry is crucial to show its unitarity. The BRST symmetry of Chern-Simons theory has been thoroughly investigated [31,32] and the BRST symmetry of N = 1 super-Chern-Simons theory has also been studied in the superspace formalism [33,34]. The BRST invariance of ABJM theory has also been studied [35].…”

Harmonic Superspace Gaugeon Formalism for the Abjm Theory

“…The BRST symmetry for ordinary Chern-Simons theory has been throughly studied [21]- [22]. In fact, the BRST symmetry of N = 1 Chern-Simons theory has also been analysed [23,24].…”