The holomorphic geometry of closed bosonic string theory and Diff S1/S1

Bowick, Mark J.; Rajeev, S. G.

doi:10.1016/0550-3213(87)90076-9

Cited by 133 publications

(74 citation statements)

References 49 publications

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“…In fact in [15] the coadjoint orbits of the Virasoro group are related to the phase space of AdS 3 gravity. However, in both the bosonic and supersymmetric cases only certain orbits admit Kähler structures and hence have a symplectic structure that can be geometrically quantized [11,16,17]. The origin of the obstruction to quantization could be due to the restrictions on the diffeomorphism field D AB which foliates the dual space into orbits.…”

Section: Resultsmentioning

confidence: 99%

Supergravitons interacting with the super-Virasoro group

Gates

Rodgers

2001

Physics Letters B

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Section: Resultsmentioning

confidence: 99%

Supergravitons interacting with the super-Virasoro group

Gates

Rodgers

2001

Physics Letters B

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“…The geometry of this infinite-dimensional space has been of interest to physicists (e.g. [8], [7], [19]). …”

Section: Introductionmentioning

confidence: 99%

“…We follow the approach taken in [8,7,19,14] in that we describe the space Diff(S 1 )/S 1 as an infinite dimensional complex manifold with a Kähler metric. Theorem 3.3 describes properties of the Hermitian and Riemannian metrics, as well as of the complexified symplectic form.…”

Section: Introductionmentioning

confidence: 99%

Riemannian geometry of Diff(S¹)/S¹ revisited

Gordina¹

2007

Stochastic Analysis in Mathematical Physics

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Abstract. A further study of Riemannian geometry Diff(S 1 )/S 1 is presented. We describe Hermitian and Riemannian metrics on the complexification of the homogeneous space, as well as the complexified symplectic form. It is based on the ideas from [12], where instead of using the Kähler structure symmetries to compute the Ricci curvature, the authors rely on classical finite-dimensional results of Nomizu et al on Riemannian geometry of homogeneous spaces.

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“…The similar methods to those used in Ref. [18] for the asymptotically anti-de Sitter space-time, e.g., geometric quantization method [26,27,28,29], are applied to the case of de Sitter gravity. There is an essential difference between these two cases.…”

Section: Quantization Of De Sitter Gravitymentioning

confidence: 99%

Comments on quantum aspects of three-dimensional de Sitter gravity

Umetsu

Yokoi

2003

Nuclear Physics B

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We investigate the quantum aspects of three-dimensional gravity with a positive cosmological constant. The reduced phase space of the three-dimensional de Sitter gravity is obtained as the space which consists of the Kerr-de Sitter space-times and their Virasoro deformations. A quantization of the phase space is carried out by the geometric quantization of the coadjoint orbits of the asymptotic Virasoro symmetries. The Virasoro algebras with real central charges are obtained as the quantum asymptotic symmetries. The states of globally de Sitter and point particle solutions become the primary states of the unitary irreducible representations of the Virasoro algebras. It is shown that those states are perturbatively stable at the quantum level. The Virasoro deformations of these solutions correspond to the excited states in the unitary irreducible representations. In view of the dS/CFT correspondence, we also study the relationship between the Liouville field theory obtained by a reduction of the SL(2;C) Chern-Simons theory and the three-dimensional gravity both classically and quantum mechanically. In the analyses of the both theories, the Kerr-de Sitter geometries with nonzero angular momenta do not give the unitary representations of the Virasoro algebras. * umetsu@post.kek.jp and umetsu@nbi.dk † yokoi@icrr.u-tokyo.ac.jp

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The holomorphic geometry of closed bosonic string theory and Diff S1/S1

Cited by 133 publications

References 49 publications

Supergravitons interacting with the super-Virasoro group

Supergravitons interacting with the super-Virasoro group

Riemannian geometry of Diff(S¹)/S¹ revisited

Comments on quantum aspects of three-dimensional de Sitter gravity

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The holomorphic geometry of closed bosonic string theory and Diff S1/S1

Cited by 133 publications

References 49 publications

Supergravitons interacting with the super-Virasoro group

Supergravitons interacting with the super-Virasoro group

Riemannian geometry of Diff(S1)/S1 revisited

Comments on quantum aspects of three-dimensional de Sitter gravity

Contact Info

Product

Resources

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Riemannian geometry of Diff(S¹)/S¹ revisited