Extended BRS symmetry in non-Abelian gauge theories

Bonora, L.; Pasti, P.; Tonin, M.

doi:10.1007/bf02812376

Cited by 66 publications

(201 citation statements)

References 18 publications

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“…In this connection, first of all, we generalize the 2D ordinary theory onto (2, 2)-dimensional supermanifold, where the nonAbelian 1-form gauge field ( ) and (anti)ghost fields ( ) are generalized onto their corresponding superfields with the following expansions (incorporating the secondary fields , , , 1 , 2 , 1 , 2 , , ) on the (2, 2)-dimensional supermanifolds [4,5]:…”

Section: Horizontality Condition: Off-shell Nilpotent (Anti-)brst Symmentioning

confidence: 99%

“…The superfield approach to BRST formalism [1][2][3][4][5][6][7][8] provides the geometrical basis for the properties of nilpotency and absolute anticommutativity which are associated with the (anti-)BRST symmetries. In the above usual superfield approach [1][2][3][4][5][6][7][8], the celebrated horizontality condition (HC) plays a key and decisive role.…”

Section: Introductionmentioning

confidence: 99%

“…In the above usual superfield approach [1][2][3][4][5][6][7][8], the celebrated horizontality condition (HC) plays a key and decisive role. The HC leads, however, to the derivation (as well as geometrical interpretation) of the (anti-)BRST symmetries that are associated with the gauge and corresponding (anti)ghost fields only.…”

Section: Introductionmentioning

confidence: 99%

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

Kumar

Chauhan

Malik

2018

Advances in High Energy Physics

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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.

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Section: Horizontality Condition: Off-shell Nilpotent (Anti-)brst Symmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Kumar

Chauhan

Malik

2018

Advances in High Energy Physics

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“…Second, the ideas of ACSA to BRST formalism are simple and straightforward and they lend support to the augmented version of superfield approach (AVSA) to BRST formalism which is based on the more formal and precise mathematical foundations (see, e.g. [4,5,[9][10][11][12]16]). Our present work, once again, establishes the validity of this observation where there is a complete agreement between our results (with ACSA) and that of the AVSA to BRST formalism.…”

Section: Introductionmentioning

confidence: 99%

Nilpotent charges in an interacting gauge theory and an 𝒩 = 2 SUSY quantum mechanical model: (Anti-)chiral superfield approach

Chauhan

Kumar

Malik

2019

Int. J. Mod. Phys. A

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We exploit the power and potential of the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the nilpotent (anti-) BRST symmetry transformations for any arbitrary D-dimensional interacting non-Abelian 1-form gauge theory where there is an SU(N) gauge invariant coupling between the gauge field and the Dirac fields. We derive the conserved and nilpotent (anti-)BRST charges and establish their nilpotency and absolute anticommutativity properties within the framework of ACSA to BRST formalism. The clinching proof of the absolute anticommutativity property of the conserved and nilpotent (anti-)BRST charges is a novel result in view of the fact that we consider, in our present endeavor, only the (anti-)chiral super expansions of the superfields that are defined on the (D, 1)-dimensional super-submanifolds of the general (D, 2)-dimensional supermanifold on which our D-dimensional ordinary interacting non-Abelian 1-form gauge theory is generalized. To corroborate the novelty of the above result, we apply the ACSA to an N = 2 supersymmetric (SUSY) quantum mechanical (QM) model of a harmonic oscillator and show that the nilpotent and conserved N = 2 super charges of this system do not absolutely anticommute.Keywords: (Anti-)chiral superfield approach; interacting non-Abelian 1-form gauge theory with Dirac fields; (anti-)BRST symmetries; (anti-)BRST charges; N = 2 SUSY harmonic oscillator; N = 2 SUSY symmetries; N = 2 SUSY charges, (anti-)chiral supervariable approach; nilpotency property; absolute anticommutativity property * The beauty of the (anti-)chiral superfield/supervariable approach is the observation that we obtain the (anti-)BRST symmetries for all the fields/variables of the theory from the (anti-)BRST (i.e. quantum gauge) invariant restrictions on the (anti-)chiral superfileds/supervariables.

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“…However, presently we leave the proof of the same for later work, and we limit ourselves to the treelevel dynamics, with physical states identified. To this end, the corresponding Faddeev-Popov ghosts [20] are identified, with invariance under two independent supersymmetric transformations, BRST and anti-BRST [21][22][23][24], which are both nilpotent and anticommuting. This enables us to identify the effective physical degrees of freedom of the theory, represented by a graviton and a massive gauge particle, with no dynamics for the scalar field.…”

Section: Introductionmentioning

confidence: 99%

Novel symmetries in Weyl-invariant gravity with massive gauge field

2016

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The background field method is used to linearize the Weyl-invariant scalar-tensor gravity, coupled with a Stückelberg field. For a generic background metric, this action is found not to be invariant, under both a diffeomorphism and generalized Weyl symmetry, the latter being a combination of gauge and Weyl transformations. Interestingly, the quadratic Lagrangian, emerging from a background of Minkowski metric, respects both transformations independently. The Becchi-Rouet-Stora-Tyutin symmetry of scalar-tensor gravity coupled with a Stückelberg-like massive gauge particle, possessing a diffeomorphism and generalized Weyl symmetry, reveals that in both cases negativenorm states with unphysical degrees of freedom do exist. We then show that, by combining diffeomorphism and generalized Weyl symmetries, all the ghost states decouple, thereby removing the unphysical redundancies of the theory. During this process, the scalar field does not represent any dynamic mode, yet modifies the usual harmonic gauge condition through non-minimal coupling with gravity.

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Extended BRS symmetry in non-Abelian gauge theories

Cited by 66 publications

References 18 publications

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

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

Nilpotent charges in an interacting gauge theory and an 𝒩 = 2 SUSY quantum mechanical model: (Anti-)chiral superfield approach

Novel symmetries in Weyl-invariant gravity with massive gauge field

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