Some remark on consistent anomalies in gauge theories

Sorella, S. P.; Tătaru, L.

doi:10.1016/0370-2693(94)90205-4

Cited by 31 publications

(16 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In other word using the operator δ we can calculate the solution of the cohomology H(s mod d) if we know the solution of the cohomology H(s). Actually, as has been shown in [23], the cocycles obtained by the descent equations (3.4) turn out to be completely equivalent to those one based on the Russian formula.…”

Section: )mentioning

confidence: 70%

“…In order to solve the tower (3.4) we shall make use of the following identity e δ s = (s + d)e δ , (3.8) which is a direct consequence of (3.7) (see [23]).…”

Section: )mentioning

confidence: 99%

“…In section 3 we define the linear operator δ and we find out a solution of the descent equations by using this operator and the general method presented in Ref. [23]. Some explicit examples are presented in section 4 and a brief discussion about the commutation properties of the δ-operator can be found in section 5.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Algebraic structure of gravity in Ashtekar’s variables

et al. 1995

View full text Add to dashboard Cite

The BRST transformations for gravity in Ashtekar's variables are obtained by using the MaurerCartan horizontality conditions. The BRST cohomology in Ashtekar's variables is calculated with the help of an operator S introduced by Sorella [Commun. Math. Phys. 157, 231 (1993)], which allows one to decompose the exterior derivative as a BRST commutator. The BRST cohomology leads to the differential invariants for four-dimensional manifolds.PACS number(s): 04.6O.Ds, 02.40.Re, 11.30.Ly I. I N T R O D U C T I O NA great amount of work has been done recently in the reformulation of general relativity in terms of a new set of variables that replace the spacetime metric [2]. These new variables, called Ashtekar's variables, have been intensively used in a large number of problems in gravitational physics. Ashtekar's main task was the quantum gravity issue and these new variables, indeed, have opened a novel line of approach to it.In any quantum field theory, one of the most important questions is the existence and t,he form of the anomalies. The anomalies, as well as the Schwinger terms and the invariant Lagrangians, could be calculated in a purely algebraic way by solving the Wess-Zumino consistency condition [3], which is equivalent to a tower of descent equations, involving the nilpotent Becchi-Rouet-StoraTyutin (BRST) operator s, as well as the exterior spacetime derivative d.The usual procedure for solving the descent equations is based on the formula of Baulieu and co-workers and the transgression equation [4] (see also . However, for the gravity in Ashtekar's variables it is difficult to write down these equations and it is necessary to follow a different scheme.First, for the Ashtekar variables, the BRST transformations [14] are different from those obtained in the Yang-Mills case. In addition, the formula of Baulieu and co-workers in the form given for the Yang-Mills case 151, does not hold and we have to find a new method for obtaining a generalization of it in this case. On the other hand, for the Ashtekar variables, as well as for the gravity with torsion [15], it is difficult to write down a transgression equation and to obtain the anomalies, the Schwinger *Permanent address: Dept. Theor. Phys., University of Cluj, Romania. terms, and the invariant Lagrangians. All these quantities are BRST invariants modulo d-exact terms and they can be obtained by using an operator 6 which allows one to express the exterior derivative d as a BRST commutator [I]:Once the decomposition (1.1) has been found, successive applications of the operator 6 on a polynomial Q which is a nontrivial solution of the equationgive an explicit nontrivial member of the BRST cohomology group modulo d-closed terms.The solving of Eq. (1.2) is a problem of local BRST cohomology instead of a modulo d one. Therefore we see that, due to the operator 6, the study of the cohomology of s modulo d can be reduced to the study of the local cohomology of s which, in turn, could be analyzed by using the spectral sequences method [16].In this paper we prove t...

show abstract

Section: )mentioning

confidence: 70%

“…In order to solve the tower (3.4) we shall make use of the following identity e δ s = (s + d)e δ , (3.8) which is a direct consequence of (3.7) (see [23]).…”

Section: )mentioning

confidence: 99%

See 1 more Smart Citation

Algebraic structure of gravity in Ashtekar’s variables

et al. 1995

View full text Add to dashboard Cite

show abstract

“…The operator δ can be used to solve the descent equations (1.2). As it has been shown in [17,18,19] these solutions can be obtained from the equation…”

Section: Brst Symmetry For the Superstringmentioning

confidence: 99%

BRST Cohomology of the Superstring in Super-Beltrami Parametrization

Tătaru

Vancea

1997

Mod. Phys. Lett. A

View full text Add to dashboard Cite

show abstract

“…We can collect then, following [31], all the Ω G+N −p where the cocycle Ω G+N 0 , according to its zero form degree, depends only on the set of zero form variables (ω a bm , R a bmn , T a mn , θ a b , η a ) and their tangent space derivatives ∂ m . Taking into account that under the action of the operator δ the form degree and the ghost number are respectively raised and lowered by one unit and that in a space-time of dimension N a (N +1)form identically vanishes, it follows that eq.…”

Section: Weyl Invariant Scalar Field Lagrangiansmentioning

confidence: 99%

Algebraic structure of gravity with torsion

Moritsch

Schweda

Sorella

1994

Class. Quantum Grav.

View full text Add to dashboard Cite

The BRS transformations for gravity with torsion are discussed by using the Maurer-Cartan horizontality conditions. With the help of an operator δ which allows to decompose the exterior space-time derivative as a BRS commutator we solve the Wess-Zumino consistency condition corresponding to invariant Lagrangians and anomalies. * Supported in part by the "Fonds zur Förderung der wissenschaftlichen Forschung" under Grant No. P9116-PHY.† Supported in part by the "Fonds zur Förderung der wissenschaftlichen Forschung", M008-Lise Meitner Fellowship.

show abstract

Some remark on consistent anomalies in gauge theories

Abstract: The new method for solving the descent equations for gauge theories proposed in [1] is shown to be equivalent with that based on the "Russian formula". Moreover it allows to obtain in a closed form the expressions of the consistent anomalies in any space-time dimension.

Cited by 31 publications

References 31 publications

Algebraic structure of gravity in Ashtekar’s variables

Algebraic structure of gravity in Ashtekar’s variables

BRST Cohomology of the Superstring in Super-Beltrami Parametrization

Algebraic structure of gravity with torsion

Contact Info

Product

Resources

About