On the algebraic characterization of witten's topological Yang-Mills theory

Ouvry, Stéphane; Stora, R.; Baal, Pierre van

doi:10.1016/0370-2693(89)90029-4

Cited by 121 publications

(97 citation statements)

References 12 publications

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“…We adopt here the standard construction of refs. [17,18,19] and introduce the following set of fields: a gauge connection A a µ , an anticommuting vector field ψ a µ (also called topological ghost), a pair of antiself-dual tensor fields (B a µν , χ a µν ) and two ghost fields (c a , ϕ a ). One needs also a couple of Lagrange multipliers (b a , η a ) and a couple of antighosts (c a ,φ a ).…”

Section: The Classical Action and The Landau Gaugementioning

confidence: 99%

A renormalized supersymmetry in the topological Yang-Mills field theory

et al. 1994

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Section: The Classical Action and The Landau Gaugementioning

confidence: 99%

A renormalized supersymmetry in the topological Yang-Mills field theory

et al. 1994

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“…Generators generated by the first two functions coincide with the corresponding generators of the standard BRST model (arising in the 4d topological Yang-Mills theory [7]) to which the Kalkman model is reduced at t = 1. The function D 1 generates the differential different from the standard BRST onê…”

Section: Models For Equivariant Cohomologymentioning

confidence: 97%

Antibrackets and Non-Abelian Equivariant Cohomology

Nersessian

1995

Mod. Phys. Lett. A

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“…The algebra Ω(M ) ⊗ W(g) and the differential (21) form the BRST model of equivariant cohomology [12,30]. However, this complex is a model for M × EG (hence its cohomology is equal to H…”

Section: The Algebroid Structure Of [−1]t a Is As Follows The Anchormentioning

confidence: 99%

Q-algebroids and their cohomology

Mehta¹

2009

Journal of Symplectic Geometry

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Abstract. A Q-algebroid is a Lie superalgebroid equipped with a compatible homological vector field and is the infinitesimal object corresponding to a Q-groupoid. We associate to every Q-algebroid a double complex. As a special case, we define the BRST model of a Lie algebroid, which generalizes the BRST model for equivariant cohomology. We extend to this setting the Mathai-Quillen-Kalkman isomorphism of the BRST and Weil models, and we suggest a definition of a basic subcomplex which, however, requires a choice of a connection. Other examples include Roytenberg's homological double of a Lie bialgebroid, Ginzburg's model of equivariant Lie algebroid cohomology, the double of a Lie algebroid matched pair, and Q-algebroids arising from lifted actions on Courant algebroids. Since a bundle map A −→ A ′ does not, in general, induce a map of sections Contentsthe differential graded algebra formulation has the distinction of being the point of view where the notion of morphism is obvious. This fact has been useful in making sense of categorical constructs involving Lie algebroids, even though a Lie algebroid structure cannot be described abstractly in terms of objects and morphisms. For example, Roytenberg [32] generalized the homological approach to Lie bialgebras [14,17] to give a homological compatibility condition for Lie bialgebroids. More recently, Voronov [38] generalized this idea further, giving a homological compatibility condition for double Lie algebroids [20].This paper deals with a closely related notion of categorical double, namely that of a Q-algebroid. A Q-algebroid may be thought of as a Lie algebroid in the category of Q-manifolds (or vice versa). As mentioned above, certain Q-manifolds are associated to Lie algebroids. Q-manifolds also arise from L ∞ -algebras [16] and in relation to the quantization of gauge systems (see, e.g. [11]).To any Q-algebroid, we can associate a double complex that is essentially the complex for Lie algebroid cohomology, "twisted" by the homological vector field. A first example is the "odd tangent algebroid . In this setting, the isomorphism of Mathai-Quillen [25] and Kalkman [12], which relates the two models, takes a surprisingly simple, coordinate-free form. Moreover, Kalkman's one-parameter family [12] that interpolates between the Weil and BRST models is immediately apparent in this context. 1 We are aware of independent work by Abad and Crainic [1], where a Lie algebroid generalization of the Weil model is given without using the language of supergeometry. Q-ALGEBROIDS AND THEIR COHOMOLOGY 3The Weil and BRST complexes are both models for Ω(M × EG). In order to obtain equivariant cohomology 2 , one must first restrict to a subcomplex of forms that are basic for the G-action; it is this step that presents a problem in the general situation, as there does not seem to be a natural choice of a basic subcomplex of Ω ([−1]A). However, if we choose a linear connection on A, then we may define a basic subcomplex that, in the case of the canonical connection on M ×g, agrees...

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On the algebraic characterization of witten's topological Yang-Mills theory

Cited by 121 publications

References 12 publications

A renormalized supersymmetry in the topological Yang-Mills field theory

A renormalized supersymmetry in the topological Yang-Mills field theory

Antibrackets and Non-Abelian Equivariant Cohomology

Q-algebroids and their cohomology

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