Perturbative aspects of the Chern-Simons field theory

Guadagnini, Enore; Martellini, M.; Mintchev, Mihail

doi:10.1016/0370-2693(89)91291-4

Cited by 143 publications

(175 citation statements)

References 13 publications

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“…Several groups have undertaken the computation of the one-loop effective action by using a number of regularization methods [18][19][20][21][22][23]. The picture that has emerged from these calculations is that every BRS-invariant regularization method [6,[19][20][21] gives for the gauge-invariant part of the one-loop effective action the CS term with coefficient k + N, k (> 0) being the bare or classical CS parameter.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the bare parameter k is shifted to k + N for all BRS-invariant regulators used as yet. On the other hand, this shift fails to occur for regularization methods that are not gauge-invariant [18,24]. One-loop results suggest therefore that BRSinvariant regulators will naturally provide a monodromy parameter k + N (k > 0), as non-perturbtive results demand.…”

Section: Introductionmentioning

confidence: 99%

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Chern-Simons theory as the large-mass limit of topologically massive Yang-Mills theory

1992

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We study quantum Chern-Simons theory as the large mass limit of the limit D → 3 of dimensionally regularized topologically massive YangMills theory. This approach can also be interpreted as a BRS-invariant hybrid regularization of Chern-Simons theory, consisting of a highercovariant derivative Yang-Mills term plus dimensional regularization.Working in the Landau gauge, we compute radiative corrections up to second order in perturbation theory and show that there is no two-loop correction to the one-loop shift k → k + c V , k being the bare ChernSimons parameter. In passing we also prove by explicit computation that topologically massive Yang-Mills theory is UV finite.2

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Chern-Simons theory as the large-mass limit of topologically massive Yang-Mills theory

1992

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“…The perturbative analysis [46,17,2,5] has also led to this result and has shown to provide a very useful framework to study Vassiliev invariants [54,20,18,3,4] (see [56] for a brief review). An important set of theories of Schwarz type are the BF theories [48].…”

Section: Topological Quantum Field Theorymentioning

confidence: 99%

“…In the case of Chern-Simons gauge theory, non-perturbative methods have been applied to obtain properties [89,41] of knot and link invariants, as well as general procedures for their computation [73,53,68]. Perturbative methods have also been studied for this theory [46,7,17,2,5] providing integral representations for Vassiliev [84] invariants [54,18,3,4]. In Donaldson-Witten theory perturbative methods have proved its relation to Donaldson invariants.…”

Section: Introductionmentioning

confidence: 99%

Lectures on topological quantum field theory

Labastida

Lozano

1998

AIP Conference Proceedings

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In these lectures we present a general introduction to topological quantum field theories. These theories are discussed in the framework of the Mathai-Quillen formalism and in the context of twisted N = 2 supersymmetric theories. We discuss in detail the recent developments in Donaldson-Witten theory obtained from the application of results based on duality for N = 2 supersymmetric Yang-Mills theories. This involves a description of the computation of Donaldson invariants in terms of Seiberg-Witten invariants. Generalizations of Donaldson-Witten theory are reviewed, and the structure of the vacuum expectation values of their observables is analyzed in the context of duality for the simplest case.

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“…We observed in [19] that the generalization of the integral or geometrical knot invariant first proposed in [22] and further analyzed in [14], as well as the invariant itself, are Vassiliev invariants. These invariants arise naturally in the perturbative analysis of the Wilson loop.…”

Section: Introductionmentioning

confidence: 99%

Vassiliev invariants for links from Chern-Simons perturbation theory

Álvarez¹,

Labastida²,

Pérez³

1997

Nuclear Physics B

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The general structure of the perturbative expansion of the vacuum expectation value of a product of Wilson-loop operators is analyzed in the context of Chern-Simons gauge theory. Wilson loops are opened into Wilson lines in order to unravel the algebraic structure encoded in the group factors of the perturbative series expansion. In the process a factorization theorem is proved for Wilson lines. Wilson lines are then closed back into Wilson loops and new link invariants of finite type are defined. Integral expressions for these invariants are presented for the first three primitive ones of lower degree in the case of two-component links. In addition, explicit numerical results are obtained for all two-component links of no more than six crossings up to degree four.

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Perturbative aspects of the Chern-Simons field theory

Cited by 143 publications

References 13 publications

Chern-Simons theory as the large-mass limit of topologically massive Yang-Mills theory

Chern-Simons theory as the large-mass limit of topologically massive Yang-Mills theory

Lectures on topological quantum field theory

Vassiliev invariants for links from Chern-Simons perturbation theory

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