Bosonized actions for anomalous gauge theories on coadjoint orbits

Bar-Moshe, David; Marinov, M. S.; Oz, Yaron

doi:10.1016/0370-2693(91)90406-g

Physics Letters B

1991

DOI: 10.1016/0370-2693(91)90406-g

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Bosonized actions for anomalous gauge theories on coadjoint orbits

David Bar-Moshe

M. S. Marinov

Yaron Oz

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1993

1994

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Cited by 3 publications

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“…Indeed, the construction of the Wess-Zumino-Novikov-Witten (WZNW) theory and two-dimensional (2D) induced gravity on coadjoint orbits of Kac-Moody and Virasoro groups, respectively, revealed a similarity in their structures, and a natural interpretation for the SL(2,R) current algebra underlying the 2D induced gravity has been found. Later on, the method of coadjoint orbits was applied to construct bosonized actions for anomalous gauge theories in two and four space-time dimensions from the extended Lie algebra generated by the Gauss-law constraints [4]. The anomalous gauge algebra determines the anomalous part of the actions.…”

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confidence: 99%

New geometrical insight into the anomalies in string theory

1994

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We apply the method of coadjoint orbits to evaluate the nonvanishing square of the BRST charge and the central extension of the Virasoro algebra from the Weyl anomaly, which is based on the basic equation satisfied by the BRST operator on a coadjoint orbit associated with string theory. PACS numberk): 11.25.Pm, 02.40.Dr, 03.65.Fd Recentlv, the construction of field theories on coad--.joint orbits of infinite-dimensional Lie groups has attracted considerable attention [I-31. Indeed, the construction of the Wess-Zumino-Novikov-Witten (WZNW) theory and two-dimensional (2D) induced gravity on coadjoint orbits of Kac-Moody and Virasoro groups, respectively, revealed a similarity in their structures, and a natural interpretation for the SL(2,R) current algebra underlying the 2D induced gravity has been found. Later on, the method of coadjoint orbits was applied to construct bosonized actions for anomalous gauge theories in two and four space-time dimensions from the extended Lie algebra generated by the Gauss-law constraints [4]. The anomalous gauge algebra determines the anomalous part of the actions. Otherwise, such a geometrical formulation has also been used to analyze the commutation relations for the Gauss-law operators in anomalous gauge theories [5]. The Becchi-Rouet-Stora-Tyutin (BRST) operator on a coadjoint orbit associated with an anomalous gauge theory satisfies a basic equation, and this equation reproduces the commutation relations for the Gauss-law operators.In this paper, we apply the method of coadjoint orbits to explore the relationship among the anomalies in the string theory. As is well known, in quantizing relativistic strings at subcritical dimensions one encounters anomalies that appear in different forms: the Weyl anomaly, the nonvanishing square of the BRST charge Q', and the Virasoro anomaly. Originally these anomalies were discovered as a result of detailed calculations which involved careful regularization of products of operators. The relationship among these anomalies has been discussed from different schemes, and most of the results can be found in Refs. [6-161. Here we shall apply the variational principle to derive Eq. (31) which relates the BRST charge with the Weyl anomaly, and exploit the basic equation satisfied by the BRST operator [5] on a coadjoint orbit associated with the string theory to evaluate the square of the BRST charge Q

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New geometrical insight into the anomalies in string theory

1994

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Quasi-invariant Lagrangians on Lie groups and the method of coadjoint orbits

Inamoto

1993

Journal of Mathematical Physics

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Starting with a two-cocycle globally defined on a Lie group G, the Lagrangian system on G is constructed whose Lagrangian is quasi-invariant under a right translation canonically lifted to the tangent bundle TG. A direct consequence of the quasi-invariance is the appearance of central extensions in the Noether-symmetry algebra. Then, it is shown that the kinematical sector of such a model realizes, through a symplectic reduction, the Kirillov–Kostant symplectic structure on the coadjoint orbit of the Lie group with the central extensions. The generalization to a ‘‘higher-dimensional’’ theory of the Wess–Zumino–Witten-type is also discussed herein.

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Gauss law commutators in anomalous gauge theories from a geometrical point of view

Kubo

1993

Phys. Rev. D

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Bosonized actions for anomalous gauge theories on coadjoint orbits

Cited by 3 publications

References 16 publications

New geometrical insight into the anomalies in string theory

New geometrical insight into the anomalies in string theory

Quasi-invariant Lagrangians on Lie groups and the method of coadjoint orbits

Gauss law commutators in anomalous gauge theories from a geometrical point of view

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