Quantum Geometry

Ambjørn, J.; Durhuus, Bergfinnur; Jónsson, Thórdur

doi:10.1017/cbo9780511524417

Cited by 290 publications

(353 citation statements)

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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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confidence: 67%

Low-energy propagation modes on string network

Sasakura¹

2001

J. High Energy Phys.

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“…[23] and [24] and the references therein.) Does the fermionic matrix-vector model play a role in quantum gravity as well?…”

Section: Quantum Orbifold Geometrymentioning

confidence: 99%

Noncommutative probability, matrix models, and quantum orbifold geometry

Lee¹

2003

J. High Energy Phys.

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Inspired by the intimate relationship between Voiculescu's noncommutative probability theory (of type A) and large-N matrix models in physics, we look for physical models related to noncommutative probability theory of type B. These turn out to be fermionic matrix-vector models at the double large-N limit. In the context of string theory, they describe different orbifolded string worldsheets with boundaries. Their critical exponents coincide with that of ordinary string worldsheets, but their renormalised tree-level one-boundary amplitudes differ.

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“…What we are saying should not be surprising in the light of analytic and numerical studies of random surface models [4]. No attempt to define strings with dimension greater than one has been successful in such studies.…”

Section: String Evolution and The Divergence Of String Amplitudesmentioning

confidence: 99%

“…In general, the expression contains a divergent piece which cannot be removed by a covariant subtraction. We believe that this divergence is related to the inability of lattice and dynamically triangulated strings to have a proper continuum limit for d > 1 [4]. The form of this divergent piece is not universal, however.…”

Section: Introductionmentioning

confidence: 96%

Evolution of fixed-end strings and the off-shell disk amplitude

Orland¹

2001

Nuclear Physics B

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An exact integral expression is found for the amplitude of a Bosonic string with ends separated by a fixed distance R evolving over a time T between arbitrary initial and final configurations. It is impossible to make a covariant subtraction of a divergent quantity which would render the amplitude non-zero. It is suggested that this fact (and not the tachyon) is responsible for the lack of a continuum limit of regularized randomsurface models with target-space dimension greater than one. It appears consistent, however, to remove this quantity by hand. The static potential of Alvarez and Arvis V (R), is recovered from the resulting finite amplitude for R > R c = π (d−2)α ′ 3 . For R < R c , we find V (R) = −∞, instead of the usual tachyonic result. A rotationinvariant expression is proposed for special cases of the off-shell disk amplitude. None of the finite amplitudes discussed are Nambu or Polyakov functional integrals, except through an unphysical analytic continuation. We argue that the Liouville field does not decouple in off-shell amplitudes, even when the space-time dimension is twenty-six. *

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Quantum Geometry

Cited by 290 publications

References 0 publications

Low-energy propagation modes on string network

Low-energy propagation modes on string network

Noncommutative probability, matrix models, and quantum orbifold geometry

Evolution of fixed-end strings and the off-shell disk amplitude

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