A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories

Achúcarro, Ana; Townsend, Paul

doi:10.1016/0370-2693(86)90140-1

Cited by 1,171 publications

(1,843 citation statements)

References 8 publications

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“…This is similar to the three-dimensional case, where pure Einstein gravity can be written as a Chern-Simons theory [5]. Apart from the gauge field, the gauge theory contains also a scalar field Φ in the adjoint of SU(1, 1).…”

Section: Two-dimensional (Anti-)de Sitter Gravity As a Topological Gamentioning

confidence: 66%

“…(4.5) describes a nonlinear σ model in 0+1 dimensions. 5 Here we used the boundary condition (3.9). 6 As we consider the universal covering space of AdS2, holonomies can be dropped.…”

Section: Boundary Terms In the Actionmentioning

confidence: 99%

“…In three dimensions, pure Einstein-AdS gravity was known to be related to a two-dimensional conformal field theory [4] even before the advent of the AdS/CFT correspondence. This is based on the fact that pure Einstein gravity in three dimensions can be written as a Chern-Simons theory [5], which is known to reduce to a WZNW model in presence of a boundary [6]. The boundary conditions for asymptotically AdS spaces [7] provide then the constraints for a hamiltonian reduction from the WZNW model to Liouville field theory [4].…”

Section: Introductionmentioning

confidence: 99%

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The Asymptotic Dynamics of two-dimensional (anti-)de Sitter Gravity

Brigante¹,

Cacciatori²,

Klemm³

et al. 2002

J. High Energy Phys.

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We show that the asymptotic dynamics of two-dimensional de Sitter or anti-de Sitter Jackiw-Teitelboim (JT) gravity is described by a generalized two-particle Calogero-Sutherland model. This correspondence is established by formulating the JT model of (A)dS gravity in two dimensions as a topological gauge theory, which reduces to a nonlinear 0+1-dimensional sigma model on the boundary of (A)dS space. The appearance of cyclic coordinates allows then a further reduction to the Calogero-Sutherland quantum mechanical model.

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Section: Two-dimensional (Anti-)de Sitter Gravity As a Topological Gamentioning

confidence: 66%

“…(4.5) describes a nonlinear σ model in 0+1 dimensions. 5 Here we used the boundary condition (3.9). 6 As we consider the universal covering space of AdS2, holonomies can be dropped.…”

Section: Boundary Terms In the Actionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Asymptotic Dynamics of two-dimensional (anti-)de Sitter Gravity

Brigante¹,

Cacciatori²,

Klemm³

et al. 2002

J. High Energy Phys.

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“…The Chern-Simons formulation [9,10] makes explict the role of local isometry invariance and also the fact that the theory is locally trivial. Sticking to the positive cosmological constant case, we can write the action in terms of an SL(2, C) connection, defined as A i a = ω i a + iℓ −1 e i a , where e i a is the dreibein and ω i a is the Lorentz dual to the spin connection.…”

Section: Chern-simons and Wess-zumino Formulations Revisitedmentioning

confidence: 99%

On the hologram of de Sitter

Cunha

2002

Phys. Rev. D

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A careful reduction of the three-dimensional gravity to the Liouville description is performed, where all gauge fixing and on-shell conditions come from the definition of asymptotic de Sitter spaces. The roles of both past and future infinities are discussed and the conditions space-time evolution imposes on both Liouville fields are explicited. Space-times which correspond to non-equivalent profiles of the Liouville field at I − and I + are shown to exist. The qualitative implications of this for any tentative dual theory are presented.

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“…Using connections as basic variables rather than metrics, the quantum theory can in fact be solved exactly in the spatially compact case for any genus. (Achucarro & Townsend (1986), Witten (1988). See also Ashtekar et al (1989) and Nelson & Regge (1989)).…”

Section: An Underlying Visionmentioning

confidence: 92%

Overview and outlook

Ashtekar¹

Canonical Gravity: From Classical to Quantum

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When you do some mountaineering...you sometimes...want to climb to some peak but there is fog everywhere...you have your map or some other indication where you probably have to go and still you are completely lost in the fog. Then...all of a sudden you see quite vaguely in the fog, just a few minute things from which you say, "Oh, this is the rock I want." In the very moment that you have seen that, then the whole picture changes completely, because although you still don't know whether you will make the rock, nevertheless for a moment you say, "... Now I know where I am; I have to go closer to that and then I will certainly find the way to go ..."

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A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories

Cited by 1,171 publications

References 8 publications

The Asymptotic Dynamics of two-dimensional (anti-)de Sitter Gravity

The Asymptotic Dynamics of two-dimensional (anti-)de Sitter Gravity

On the hologram of de Sitter

Overview and outlook

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