Global charges in Chern-Simons theory and the 2+1 black hole

Bañados, Máximo

doi:10.1103/physrevd.52.5816

Cited by 182 publications

(335 citation statements)

References 23 publications

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“…We recognize the equation for the hyperbolic functions entering the BTZ solution, but now their arguments have been generalized from ρ to h. By permuting the Lie algebra elements J i in Equations (28,29) one obtains solutions generalizing the BTZ solutions for all three regions, provided the signs in Equations (28,29,32) are changed accordingly. Matching of the regions works precisely as in the BTZ case.…”

Section: Holonomiesmentioning

confidence: 99%

“…The positions of the sources are trickier, and cannot be resolved by the holonomies. Other available observables are the asymptotic charges [28]. The general f + and f − are asymptotic to the corresponding BTZ forms, and the issue is if the approach is fast enough to give finite asymptotic charges, but also slow enough to give non-zero values.…”

Section: Gauge Transformationsmentioning

confidence: 99%

See 1 more Smart Citation

Multi-black-hole sectors ofAdS3gravity

Månsson

Sundborg

2001

Phys. Rev. D

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We construct and discuss solutions of SO(1, 2)×SO(1, 2) Chern-Simons theory which correspond to multiple BTZ black holes. These solutions typically have additional singularities, the simplest cases being special conical singularities with a 2π surplus angle. There are solutions with singularities inside a common outer horizon, and other solutions with naked conical singularities. Previously such singularities have been ruled out on physical grounds, because they do not obey the geodesic equation. We find however that the Chern-Simons gauge symmetry may be used to locate all such singularities to the horizons, where they necessarily follow geodesics. We are therefore led to conclude that these singular solutions correspond to physically sensible geometries.Boundary charges at infinity are only sensitive to the total mass and spin of the black holes, and not to the distribution among the black holes. We therefore argue that a holographic description in terms of a boundary conformal field theory should represent both single and multiple BTZ solutions with the same asymptotic charges. Then sectors with multiple black holes would contribute to the black hole entropy calculated from a boundary CFT.

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Section: Holonomiesmentioning

confidence: 99%

Section: Gauge Transformationsmentioning

confidence: 99%

Multi-black-hole sectors ofAdS3gravity

Månsson

Sundborg

2001

Phys. Rev. D

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“…Therefore, as a residual symmetry, we obtain translations, local in time, and rigid rotations (see also [30][31][32] for a similar situation in General Relativity). Putting (4.8) and (4.11) into the Chern-Simons action (see (3.5) and (3.11)) we find (modulo a total time derivative)…”

Section: Gauge Fixing and Residual Symmetrymentioning

confidence: 99%

From Gauging Nonrelativistic Translations to N-Body Dynamics

Lukierski

Stichel²,

Zakrzewski

2001

Annals of Physics

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We consider the gauging of space translations with time-dependent gauge functions. Using fixed time gauge of relativistic theory, we consider the gaugeinvariant model describing the motion of nonrelativistic particles. When we use gauge-invariant nonrelativistic velocities as independent variables the translation gauge fields enter the equations through a d × (d + 1) matrix of vielbein fields and their Abelian field strengths, which can be identified with the torsion tensors of teleparallel formulation of relativity theory. We consider the planar case (d = 2) in some detail, with the assumption that the action for the dreibein fields is given by the translational Chern-Simons term. We fix the asymptotic transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in * e-mail: lukier@ift.uni.wroc.pl † email: pstichel@gmx.de ‡ e-mail: W.J.Zakrzewski@durham.ac.uk 1 time) translations and rigid rotations. We describe the effective interaction of the d = 2 N -particle problem and discuss its classical solution for N = 2. The phase space Hamiltonian H describing two-body interactions satisfies a nonlinear equation H = H( x, p; H) which implies, after quantization, a nonstandard form of the Schrödinger equation with energy dependent fractional angular momentum eigenvalues. Quantum solutions of the two-body problem are discussed. The bound states with discrete energy levels correspond to a confined classical motion (for the planar distance between two particles r ≤ r 0 ) and the scattering states with continuum energy correspond to the classical motion for r > r 0 . We extend our considerations by introducing an external constant magnetic field and, for N = 2, provide the classical and quantum solutions in the confined and unconfined regimes.

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“…It is a natural question to see whether this algebra can be obtained from a Chern-Simons theory in five dimensions just as the Kac-Moody algebra is generated from the 2+1 Chern-Simons theory [4] (see also Ref. [20]). This problem has been already studied in the literature in interesting works that considered modifications of the ChernSimons action.…”

Section: Global Symmetries and Wzw 4 Algebrasmentioning

confidence: 99%

“…These constraints are given by 20) and they generate the spatial diffeomorphisms (2.3), namely, δA a i = {A a i , Σ η j H j } = −η j F ij . Thus, they satisfy the spatial diffeomorphism algebra, up to gauge transformations.…”

Section: First Class Constraintsmentioning

confidence: 99%

The dynamical structure of higher dimensional Chern-Simons theory

1996

Self Cite

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Higher dimensional Chern-Simons theories, even though constructed along the same topological pattern as in 2+1 dimensions, have been shown recently to have generically a non-vanishing number of degrees of freedom. In this paper, we carry out the complete Dirac Hamiltonian analysis (separation of first and second class constraints and calculation of the Dirac bracket) for a group G × U (1). We also study the algebra of surface charges that arise in the presence of boundaries and show that it is isomorphic to the WZW 4 discussed in the literature. Some applications are then considered. It is shown, in particular, that Chern-Simons gravity in dimensions greater than or equal to five has a propagating torsion.

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Global charges in Chern-Simons theory and the 2+1 black hole

Cited by 182 publications

References 23 publications

Multi-black-hole sectors ofAdS3gravity

Multi-black-hole sectors ofAdS3gravity

From Gauging Nonrelativistic Translations to N-Body Dynamics

The dynamical structure of higher dimensional Chern-Simons theory

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