Non-associative gauge theory and higher spin interactions

Medeiros, Paul de; Ramgoolam, Sanjaye

doi:10.1088/1126-6708/2005/03/072

Cited by 19 publications

(19 citation statements)

References 87 publications

(188 reference statements)

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“…While a usual continuous space can be characterized by a commutative and associative algebra of functions, a noncommutative space for instance can be characterized by a noncommutative associative algebra. One may even consider a nonassociative algebra to define a nonassociative space [48][49][50][51].…”

Section: A Brief Overview Of Tensor Modelsmentioning

confidence: 99%

Canonical Tensor Models With Local Time

Sasakura

2012

Int. J. Mod. Phys. A

100

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It is an intriguing question how local time can be introduced in the emergent picture of spacetime. In this paper, this problem is discussed in the context of tensor models. To consistently incorporate local time into tensor models, a rankthree tensor model with first class constraints in Hamilton formalism is presented. In the limit of usual continuous spaces, the algebra of constraints reproduces that of general relativity in Hamilton formalism. While the momentum constraints can be realized rather easily by the symmetry of the tensor models, the form of the Hamiltonian constraints is strongly limited by the condition of the closure of the whole constraint algebra. Thus the Hamiltonian constraints have been determined on the assumption that they are local and at most cubic in canonical variables. The form of the Hamiltonian constraints has similarity with the Hamiltonian in the c < 1 string field theory, but it seems impossible to realize such a constraint algebras in the framework of vector or matrix models. Instead these models are rather useful as matter theories coupled with the tensor model. In this sense, a three-index tensor is the minimum-rank dynamical variable necessary to describe gravity in terms of tensor models.

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Section: A Brief Overview Of Tensor Modelsmentioning

confidence: 99%

Canonical Tensor Models With Local Time

Sasakura

2012

Int. J. Mod. Phys. A

100

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“…Covariant higher-dimensional fuzzy spaces were studied e.g. in [2,4,6,54,[88][89][90][91][92][93][94][95], which are similar in spirit to Snyder space [41,96], see also [47] for a somewhat related ansatz. In particular, the relation of fuzzy S 4 to fuzzy CP 2 was pointed out in [5,97,98], which is analogous to the bundle structure discussed in section 5.…”

Section: Further Literaturementioning

confidence: 99%

On the quantum structure of space-time, gravity, and higher spin in matrix models

Steinacker

2020

Class. Quantum Grav.

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In this introductory review, we argue that a quantum structure of space-time naturally entails a higher-spin theory, to avoid significant Lorentz violation. A suitable framework is provided by Yang-Mills matrix models, which allow to consider space-time as a physical system, which is treated on the same footing as the fields that live on it. We discuss a specific quantum space-time solution, whose internal structure leads to a consistent and ghost-free higher-spin gauge theory. The spin 2 modes give rise to metric perturbations, which include the standard gravitons as well as the linearized Schwarzschild solution.

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“…In fact, the K ab in (25) should be replaced with its logarithm for a direct link to (23). Moreover K ab in (25) may be replaced with another rank-two symmetric tensor obtained from C abc and g ab .…”

Section: The Modelmentioning

confidence: 99%

“…Therefore, though its relation to quantization of spacetime is not clear, it would be fair to say that nonassociativity is also another physically sensible structure of spacetime. Moreover, it is generally much easier to obtain commutative nonassociative fuzzy spaces of physical interest [22,23] than noncommutative ones which seem to generally require a kind of symplectic structure. In addition, quantum field theory on commutative nonassociative spacetimes seems to be able to respect the principles in physics more faithfully [24] than noncommutative quantum field theory, which is known to have some unusual properties such as the UV/IR mixing [25,26] and the violation of causality [27] and unitarity [28].…”

Section: Introductionmentioning

confidence: 99%

Tensor model and dynamical generation of commutative non-associative fuzzy spaces

Sasakura

2006

Class. Quantum Grav.

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Rank-three tensor model may be regarded as theory of dynamical fuzzy spaces, because a fuzzy space is defined by a three-index coefficient of the product between functions on it, f a * f b = C ab c f c . In this paper, this previous proposal is applied to dynamical generation of commutative nonassociative fuzzy spaces. It is numerically shown that fuzzy flat torus and fuzzy spheres of various dimensions are classical solutions of the rank-three tensor model. Since these solutions are obtained for the same coupling constants of the tensor model, the cosmological constant and the dimensions are not fundamental but can be regarded as dynamical quantities. The symmetry of the model under the general linear transformation can be identified with a fuzzy analog of the general coordinate transformation symmetry in general relativity. This symmetry of the tensor model is broken at the classical solutions. This feature may make the model to be a concrete finite setting for applying the old idea of obtaining gravity as Nambu-Goldstone fields of the spontaneous breaking of the local translational symmetry.

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Non-associative gauge theory and higher spin interactions

Cited by 19 publications

References 87 publications

Canonical Tensor Models With Local Time

Canonical Tensor Models With Local Time

On the quantum structure of space-time, gravity, and higher spin in matrix models

Tensor model and dynamical generation of commutative non-associative fuzzy spaces

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