The Batalin–Vilkovisky formalism description of self-dual Chern–Simons gauge theory coupled to matter fields in superspace

2020 ◽  
Vol 35 (05) ◽  
pp. 2050020
Author(s):  
Jialiang Dai
Keyword(s):  
Gauge Theory ◽  
Lagrangian Density ◽  
Brst Symmetry ◽  
Scalar Fields ◽  
Covariant Form ◽  
Brst Transformation ◽  
Shift Symmetry ◽  
Chern Simons ◽  
Matter Fields

We construct the extended BRST and anti-BRST transformation by considering a shift symmetry both in Abelian and non-Abelian Chern–Simons theories coupled to scalar fields using the approach of Batalin–Vilkovisky quantization. The extended BRST invariant Lagrangian density is able to be addressed in the framework of superfield formalism with one fermionic coordinate. In the case of extended BRST–anti-BRST symmetry, it is shown that the Batalin–Vilkovisky action of the theory can be expressed in a covariant form with two fermionic coordinates in the superspace.

scholarly journals SUPERFIELD APPROACH TO A NOVEL SYMMETRY FOR NON-ABELIAN GAUGE THEORY

2002 ◽  
Vol 17 (03) ◽  
pp. 185-196 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Lagrangian Density ◽  
Brst Symmetry ◽  
Geometrical Interpretation ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Conserved Charges ◽  
Continuous Symmetries ◽  
Matter Fields

In the framework of superfield formalism, we demonstrate the existence of a new local, covariant, continuous and nilpotent (dual-BRST) symmetry for the BRST invariant Lagrangian density of a self-interacting two (1+1)-dimensional (2D) non-Abelian gauge theory (having no interaction with matter fields). The local and nilpotent Noether conserved charges corresponding to the above continuous symmetries find their geometrical interpretation as the translation generators along the odd (Grassmannian) directions of the four (2+2)-dimensional compact supermanifold.

scholarly journals Superfield Approach to Nilpotency and Absolute Anticommutativity of Conserved Charges: 2D Non-Abelian 1-Form Gauge Theory

2018 ◽  
Vol 2018 ◽  
pp. 1-23 ◽  
Author(s):  
S. Kumar ◽  
B. Chauhan ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
Brst Symmetry ◽  
Theoretical Strength ◽  
Conserved Charges ◽  
Lagrangian Densities ◽  
Matter Fields ◽  
Chiral Superfields

We exploit the theoretical strength of augmented version of superfield approach (AVSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism to express the nilpotency and absolute anticommutativity properties of the (anti-)BRST and (anti-)co-BRST conserved charges for the two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields) in the language of superspace variables, their derivatives, and suitable superfields. In the proof of absolute anticommutativity property, we invoke the strength of Curci-Ferrari (CF) condition for the (anti-)BRST charges. No such outside condition/restriction is required in the proof of absolute anticommutativity of the (anti-)co-BRST conserved charges. The latter observation (as well as other observations) connected with (anti-)co-BRST symmetries and corresponding conserved charges are novel results of our present investigation. We also discuss the (anti-)BRST and (anti-)co-BRST symmetry invariance of the appropriate Lagrangian densities within the framework of AVSA. In addition, we dwell a bit on the derivation of the above fermionic (nilpotent) symmetries by applying the AVSA to BRST formalism, where only the (anti)chiral superfields are used.

HAMILTONIAN BRST QUANTIZATION OF CHERN-SIMONS GAUGE THEORY

1990 ◽  
Vol 05 (21) ◽  
pp. 1663-1670 ◽  
Author(s):  
Y. IGARASHI ◽  
H. IMAI ◽  
S. KITAKADO ◽  
J. KUBO ◽  
H. SO
Keyword(s):  
Gauge Theory ◽  
Brst Quantization ◽  
Hamiltonian Formalism ◽  
Constrained Systems ◽  
Three Dimensions ◽  
Brst Transformation ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Covariant Action ◽  
Chern Simons

We quantize non-abelian gauge theory with only a Chern-Simons term in three dimensions by using the generalized Hamiltonian formalism of Batalin and Fradkin for irreducible first-and second-class constrained systems, and derive a covariant action for the theory which is invariant under the off-shell nilpotent BRST transformation. Some aspects of the theory, finiteness and supersymmetry are discussed.

scholarly journals Partial Resolution of Complex Cones over Fanoℬ

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Siddharth Dwivedi ◽  
P. Ramadevi
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Special Kind ◽  
Inverse Algorithm ◽  
Quiver Gauge Theory ◽  
Partial Resolution ◽  
Chern Simons ◽  
Matter Fields

In our recent paper, we systematized an inverse algorithm to obtain quiver gauge theory living on theM2-branes probing the singularities of a special kind of Calabi-Yau fourfold which were complex cones over toric Fanoℙ3,ℬ1,ℬ2,ℬ3. These quiver gauge theories cannot be given a dimer tiling presentation. We use the method of partial resolution to show that the toric data ofℂ4and Fanoℙ3can be embedded inside the toric data of Fanoℬtheories. This method indirectly justifies that the two-node quiver Chern-Simons theories corresponding toℂ4, Fanoℙ3, and their orbifolds can be obtained by higgsing matter fields of the three-node parent quiver corresponding to Fanoℬ1,ℬ2,ℬ3,ℬ4threefold.

scholarly journals Equivalence of Chern-Simons gauge theory and WZNW model using a BRST symmetry

1999 ◽  
Vol 466 (2-4) ◽  
pp. 227-233 ◽  
Author(s):  
Jens Fjelstad ◽  
Stephen Hwang
Keyword(s):  
Gauge Theory ◽  
Brst Symmetry ◽  
Wznw Model ◽  
Chern Simons

scholarly journals NILPOTENT SYMMETRIES FOR MATTER FIELDS IN NON-ABELIAN GAUGE THEORY: AUGMENTED SUPERFIELD FORMALISM

2005 ◽  
Vol 20 (20n21) ◽  
pp. 4899-4915 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
General Scheme ◽  
Brst Symmetry ◽  
Grassmann Algebra ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Symmetry Transformations ◽  
Matter Fields ◽  
Augmented Superfield Formalism ◽  
Standing Problem

In the framework of superfield approach to Becchi–Rouet–Stora–Tyutin (BRST) formalism, the derivation of the BRST and anti-BRST nilpotent symmetry transformations for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem. In our present investigation, the local, covariant, continuous and off-shell nilpotent (anti-)BRST symmetry transformations for the Dirac fields [Formula: see text] are derived in the framework of the augmented superfield formulation where the four (3 + 1)-dimensional (4D) interacting non-Abelian gauge theory is considered on the six (4 + 2)-dimensional supermanifold parametrized by the four even space–time coordinates xμ and a couple of odd elements (θ and [Formula: see text]) of the Grassmann algebra. The requirement of the invariance of the matter (super)currents and the horizontality condition on the (super)manifolds leads to the derivation of the nilpotent symmetries for the matter fields as well as the gauge and the (anti)ghost fields of the theory in the general scheme of augmented superfield formalism.

scholarly journals Dimensional oxidization on coset space

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Koichi Harada ◽  
Pei-Ming Ho ◽  
Yutaka Matsuo ◽  
Akimi Watanabe
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Symmetry Algebra ◽  
Scalar Fields ◽  
Space Time ◽  
Coset Space ◽  
Infinite Dimensional ◽  
Gauge Algebra ◽  
The Matrix ◽  
Chern Simons

Abstract In the matrix model approaches of string/M theories, one starts from a generic symmetry gl(∞) to reproduce the space-time manifold. In this paper, we consider the generalization in which the space-time manifold emerges from a gauge symmetry algebra which is not necessarily gl(∞). We focus on the second nontrivial example after the toroidal compactification, the coset space G/H, and propose a specific infinite-dimensional symmetry which realizes the geometry. It consists of the gauge-algebra valued functions on the coset and Lorentzian generator pairs associated with the isometry. We show that the 0-dimensional gauge theory with the mass and Chern-Simons terms gives the gauge theory on the coset with scalar fields associated with H.

BRST formulation of Chern-Simons gauge theory coupled to matter fields

1992 ◽  
Vol 46 (6) ◽  
pp. 2730-2733 ◽  
Author(s):  
Hyeonjoon Shin ◽  
Won-Tae Kim ◽  
Jae-Kwan Kim ◽  
Young-Jai Park
Keyword(s):  
Gauge Theory ◽  
Chern Simons ◽  
Matter Fields

scholarly journals NON-RENORMALIZATION THEOREM FOR THE GAUGE COUPLING IN 2+1 DIMENSIONS

1994 ◽  
Vol 09 (21) ◽  
pp. 1925-1932 ◽  
Author(s):  
A.N. KAPUSTIN ◽  
P.I. PRONIN
Keyword(s):  
Gauge Theory ◽  
Gauge Field ◽  
Gauge Coupling ◽  
Scalar Fields ◽  
Field Action ◽  
Β Function ◽  
Chern Simons

We prove that the β-function of the gauge coupling in 2+1 dimensions gauge theory coupled to any renormalizable system of spinor and scalar fields is zero. This result holds both when the gauge field action is the Chern-Simons action and when it is the topologically massive action.

scholarly journals Some novel features in 2D non-Abelian theory: BRST approach

2017 ◽  
Vol 32 (22) ◽  
pp. 1750136 ◽  
Author(s):  
N. Srinivas ◽  
S. Kumar ◽  
B. K. Kureel ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
Lagrange Multipliers ◽  
Brst Symmetry ◽  
Abelian Theory ◽  
Symmetry Transformations ◽  
Lagrangian Densities ◽  
Matter Fields

Within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism, we discuss some novel features of a two (1[Formula: see text]+[Formula: see text]1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields). Besides the usual off-shell nilpotent and absolutely anticommutating (anti-)BRST symmetry transformations, we discuss the off-shell nilpotent and absolutely anticommutating (anti-)co-BRST symmetry transformations. Particularly, we lay emphasis on the existence of the coupled (but equivalent) Lagrangian densities of the 2D non-Abelian theory in view of the presence of (anti-)co-BRST symmetry transformations where we pin-point some novel features associated with the Curci–Ferrari (CF-)type restrictions. We demonstrate that these CF-type restrictions can be incorporated into the (anti-)co-BRST invariant Lagrangian densities through the fermionic Lagrange multipliers which carry specific ghost numbers. The modified versions of the Lagrangian densities (where we get rid of the new CF-type restrictions) respect some precise symmetries as well as a couple of symmetries with CF-type constraints. These observations are completely novel as far as the BRST formalism, with proper (anti-)co-BRST symmetries, is concerned.

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