Discrete and Continuum Approaches to Three-Dimensional Quantum Gravity

Ooguri, Hirosi; Sasakura, Naoki

doi:10.1142/s0217732391004140

Cited by 71 publications

(90 citation statements)

References 17 publications

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“…This boundary action is that of an obviously topological two-dimensional field theory in agreement with the proof by Ooguri and Sasakura [18] that with the 8UJ = 0 boundary condition the path sum is a topological invariant not just of the bulk but of the bulk plus boundary theory.…”

Section: Boundariessupporting

confidence: 88%

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Boundary actions in Ponzano–Regge discretization, quantum groups and $AdS_3$

O’Loughlin¹

2002

Advances in Theoretical and Mathematical Physics

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Boundary actions for three-dimensional quantum gravity in the discretized formalism of Ponzano-Regge are studied with a view towards understanding the boundary degrees of freedom. These degrees of freedom postulated in the holography hypothesis are supposed to be characteristic of quantum gravity theories. In particular it is expected that some of these degrees of freedom reside on black hole horizons. This paper is a study of these ideas in the context of a theory of quantum gravity that requires no additional structure such as supersymmetry or special gravitational backgrounds. Lorentzian as well as Euclidean regimes are examined. Some surprising relationships to Liouville theory and string theory in AdSs are found. e-print archive: http://lanl.arXiv.org/abs/gr-qc/0002092 796 Boundary actions in Ponzano-Regge discretization

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Section: Boundariessupporting

confidence: 88%

“…Let us consider the general variation of the BF action for a manifold with boundary, (other work on this subject can be found in the papers [17,18,19]). …”

Section: Boundariesmentioning

confidence: 99%

Boundary actions in Ponzano–Regge discretization, quantum groups and $AdS_3$

O’Loughlin¹

2002

Advances in Theoretical and Mathematical Physics

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“…In the present short note, we rather regard it as a space. This might be similar in spirit to the idea of brane world [5,6] and also to the network appearing in quantum gravity [7,8,9,10,11]. We shall discuss the low frequency propagation modes on it.…”

mentioning

confidence: 67%

Low-energy propagation modes on string network

Sasakura¹

2001

J. High Energy Phys.

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We study low-energy propagation modes on string network lattice. Specifically, we consider an infinite two-dimensional regular hexagonal string network and analyze the low frequency propagation modes on it. The fluctuation modes tangent to the two-dimensional plane respect the spatial rotational symmetry on the plane, and are described by Maxwell theory. The gauge symmetry comes from the marginal deformation of changing the sizes of the loops of the lattice. The effective Lorentz symmetry respected at low energy will be violated at high energy. *

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“…Section 7 is devoted to the discussion about how to incorporate gravity into our lattice formulation. This paper was inspired by the work by Turaev and Viro [10] who constructed a series of three-dimensional topological invariants by using lattice approach (see also [11]). …”

Section: Ansatz 1 the Partition Function Of Ltft Which Is First Consmentioning

confidence: 99%

Lattice topological field theory in two dimensions

1994

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The lattice definition of a two-dimensional topological field theory (TFT) is given generically, and the exact solution is obtained explicitly. In particular, the set of all lattice topological field theories is shown to be in one-to-one correspondence with the set of all associative algebras R, and the physical Hilbert space is identified with the center Z(R) of the associative algebra R. Perturbations of TFT's are also considered in this approach, showing that the form of topological perturbations is automatically determined, and that all TFT's are obtained from one TFT by such perturbations. Several examples are presented, including twisted N = 2 minimal topological matter and the case where R is a group ring. *

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Discrete and Continuum Approaches to Three-Dimensional Quantum Gravity

Cited by 71 publications

References 17 publications

Boundary actions in Ponzano–Regge discretization, quantum groups and $AdS_3$

Boundary actions in Ponzano–Regge discretization, quantum groups and $AdS_3$

Low-energy propagation modes on string network

Lattice topological field theory in two dimensions

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