Perturbative gauge theories

Baulieu, Laurent

doi:10.1016/0370-1573(85)90091-2

Cited by 231 publications

(139 citation statements)

References 106 publications

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“…and the propagator is 38) where Γ mn is the inverse of Γ mn and satisfies 40) which permits to check (3.38).…”

Section: Jhep12(2010)052mentioning

confidence: 99%

“…The anomalies associated to a linearly realised group are well known, and are classified by symmetric Casimirs. A nice way to derive such anomalies is by means of the 'Russian formula' [36][37][38][39] 29) to derive a (d + δ k )-cocycle from any symmetric Casimirs by use of the Cartan homotopy formula. In four dimensions, the relevant Casimir is the symmetric tensor of rank three, and the Cartan homotopy formula gives…”

Section: Jhep12(2010)052mentioning

confidence: 99%

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E 7(7) symmetry in perturbatively quantised $ \mathcal{N} = 8 $ supergravity

Bossard

Hillmann

Nicolai

2010

J. High Energ. Phys.

130

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Abstract:We study the perturbative quantisation of N = 8 supergravity in a formulation where its E 7(7) symmetry is realised off-shell. Relying on the cancellation of SU(8) current anomalies we show that there are no anomalies for the non-linearly realised E 7(7) either; this result extends to all orders in perturbation theory. As a consequence, the e 7(7) Ward identities can be consistently implemented and imposed at all orders in perturbation theory, and therefore potential divergent counterterms must in particular respect the full non-linear E 7(7) symmetry.

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“…and the propagator is 38) where Γ mn is the inverse of Γ mn and satisfies 40) which permits to check (3.38).…”

Section: Jhep12(2010)052mentioning

confidence: 99%

Section: Jhep12(2010)052mentioning

confidence: 99%

E 7(7) symmetry in perturbatively quantised $ \mathcal{N} = 8 $ supergravity

Bossard

Hillmann

Nicolai

2010

J. High Energ. Phys.

130

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“…The pure ghost numbers of the terms appearing in (8.7) must of course add up to 2 + q, where q is the total ghost number of a. The factors ω Γ (C) have the useful property of belonging to a chain of descent equations [20,21,22] involving at least two steps…”

Section: Solutions Of Class Imentioning

confidence: 99%

Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory

1995

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Yang-Mills models with compact gauge group coupled to matter fields are considered. The general tools developed in a companion paper are applied to compute the local cohomology of the BRST differential s modulo the exterior spacetime derivative d for all values of the ghost number, in the space of polynomials in the fields, the ghosts, the antifields (=sources for the BRST variations) and their derivatives. New solutions to the consistency conditions sa + db = 0 depending non trivially on the antifields are exhibited. For a semisimple gauge group, however, these new solutions arise only at ghost number two or higher. Thus at ghost number zero or one, the inclusion of the antifields does not bring in new solutions to the consistency condition sa + db = 0 besides the already known ones. The analysis does not use power counting and is purely cohomological. It can be easily extended to more general actions containing higher derivatives of the curvature, or Chern-Simons terms.

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“…[This vacuum is not invariant under spacetime translation of the old fields, φ ab µ andφ ab µ , because of the explicit x µ dependence in the shift (24).] Translation invariance implies that the terms ∂ i ϕ and ∂ iφ do not contribute to (39), and we obtain…”

Section: B Gap Equationmentioning

confidence: 98%

“…Introduction of the auxiliary ghost fields and of the auxiliary s-exact action (19) is legitimate in the BRST approach [39], although the reason for doing so is not yet apparent.…”

Section: Local Brst-invariant Action In Coulomb Gaugementioning

confidence: 99%

Equation of state of gluon plasma and renormalization of local action

Zwanziger¹

2007

Braz. J. Phys.

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We consider a local, renormalizable, BRST-invariant action for QCD in Coulomb gauge that contains auxiliary bose and fermi ghost fields. It possess a non-perturbative vacuum that spontaneously breaks BRSTinvariance. The vacuum condition leads to a gap equation that introduces a mass scale. Calculations are done to one-loop order in a perturbative expansion about this vacuum. They are free of the finite-T infrared divergences found by Lindé and which occur in the order g 6 corrections to the Stefan-Boltzmann equation of state. We obtain a finite result for these corrections. Renormalization and renormalization-group flow are described. We calculate the ghost propagator and color-Coulomb potential to one-loop and find that they are long range, whereas the 3-dimensionally transverse would-be physical gluon propagator is suppressed like k 2 at small |k|. These one-loop results accord with the Gribov scenario in Coulomb gauge and with recent numerical determinations of these quantities. When the auxiliary fields are integrated out, one obtains the standard Coulomb gauge action with a cut-off at the Gribov horizon.

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Perturbative gauge theories

Cited by 231 publications

References 106 publications

E 7(7) symmetry in perturbatively quantised $ \mathcal{N} = 8 $ supergravity

E 7(7) symmetry in perturbatively quantised $ \mathcal{N} = 8 $ supergravity

Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory

Equation of state of gluon plasma and renormalization of local action

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