Superspace approach to quantum gauge theories

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

doi:10.1016/0003-4916(82)90102-6

Cited by 47 publications

(185 citation statements)

References 21 publications

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“…Formulae (3.8) are determined in such a way as to match the following rheonomic parametrizations 9) that appear in the N=3 and N=2 formulations, respectively. In the N=2 notation the gaugino curvatures are 10) where…”

Section: N=2 Supergravity Plus Vector Multiplets In the Minimal mentioning

confidence: 99%

“…The equations of motion of the vector bosons can be written in the following form 9) where S Λ is, by definition, the coefficient in the lagrangian of the field strength F Λ , namely 10) and R Λ is the remainder that comes from the δ δA Λ -variation of those terms that are manifestly R-duality invariant and do not depend on the graviphoton A 0 . Since one can easily verify thatδS Λ vanishes whenever Λ = 0 (to this purpose, note thatδ(N iΣ F +ab Σ ) =δ(N iΣ F −ab Σ ) = 0 and use the explicit expressions (3.2)), then the field equations of the matter vectors are all R-duality invariant.…”

Section: Let Us Rewrite the Rheonomic Parametrization Of The Vectors mentioning

confidence: 99%

“…If gravity is external (Q(m) is Hyperkähler) then the gravitational background should be restricted by the need to have N=2 global supersymmetry, however, the proof that the solutions to the above equations are indeed instantons works for any background and is based on the following identity 9) where h ij = 2E ak i E bk j η ab is the metric of Q(m), while E ak ≡ E ak i dq i . The form E [ak ∧ E b] − k ∧ V a ∧ V b is proportional to Ω x ∧ V a ∧ V b (the coefficient, which is a numerical matrix M ab x antiselfdual in ab is not important), where Ω x are the 2-forms introduced above.…”

Section: The General Structure Of the Twisting Procedures And Quatmentioning

confidence: 99%

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Topological twist in four dimensions, R-duality and hyperinstantons

Anselmi¹,

Fré²

1993

Nuclear Physics B

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ABSTRACT. In this paper we continue the programme of topologically twisting N=2 theories in D=4, focusing on the coupling of vector multiplets to N=2 supergravity. We show that in the minimal case, namely when the special geometry prepotential F (X) is a quadratic polynomial, the theory has a so far unknown on shell U (1) symmetry, that we name R-duality. R-duality is a generalization of the chiraldual on shell symmetry of N=2 pure supergravity and of the R-symmetry of N=2super Yang-Mills theory. Thanks to this, the theory can be topologically twisted and topologically shifted, precisely as pure N=2 supergravity, to yield a natural coupling of topological gravity to topological Yang-Mills theory. The gauge-fixing condition that emerges from the twisting is the self-duality condition on the gauge field-stength and on the spin connection. Hence our theory reduces to intersection theory in the moduli-space of gauge instantons living in gravitational instanton backgrounds. We remark that, for deep properties of the parent N=2 theory, the topological Yang-Mills theory we obtain by taking the flat space limit of our gravity coupled Lagrangian is different from the Donaldson theory constructed by Witten. Whether this difference is substantial and what its geometrical implications may be is yet to be seen.We also discuss the topological twist of the hypermultiplets leading to topological quaternionic σ-models. The instantons of these models, named by us hyperinstantons, correspond to a notion of triholomorphic mappings discussed in the paper.In all cases the new ghost number is the sum of the old ghost number plus the R-duality charge. The observables described by the theory are briefly discussed.In conclusion, the topological twist of the complete N=2 theory defines intersection theory in the moduli space of gauge instantons plus gravitational instantons plus hyperinstantons. This is possibly a new subject for further mathematical investigation.2

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Section: N=2 Supergravity Plus Vector Multiplets In the Minimal mentioning

confidence: 99%

Section: Let Us Rewrite the Rheonomic Parametrization Of The Vectors mentioning

confidence: 99%

Section: The General Structure Of the Twisting Procedures And Quatmentioning

confidence: 99%

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Topological twist in four dimensions, R-duality and hyperinstantons

Anselmi¹,

Fré²

1993

Nuclear Physics B

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“…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%

“…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%

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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Grassmannian Space-Time Structure as an Origin of Gauge Symmetries

Baulieu

1988

Quantum Mechanics of Fundamental Systems 1

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Superspace approach to quantum gauge theories

Cited by 47 publications

References 21 publications

Topological twist in four dimensions, R-duality and hyperinstantons

Topological twist in four dimensions, R-duality and hyperinstantons

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

Grassmannian Space-Time Structure as an Origin of Gauge Symmetries

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