Scalar field theory on fuzzy<i>S</i><sup>4</sup>

Medina, Julieta; O’Connor, Denjoe

doi:10.1088/1126-6708/2003/11/051

Cited by 58 publications

(104 citation statements)

References 22 publications

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“…[23][24][25][26][27]. The starting point is the Lie algebra so(6) ∼ = su(4), with generators M ab , a, b = 1, .…”

Section: The Euclidean Fuzzy 4-spherementioning

confidence: 99%

Cosmological space-times with resolved Big Bang in Yang-Mills matrix models

Steinacker

2018

J. High Energ. Phys.

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We present simple solutions of IKKT-type matrix models that can be viewed as quantized homogeneous and isotropic cosmological space-times, with finite density of microstates and a regular Big Bang (BB). The BB arises from a signature change of the effective metric on a fuzzy brane embedded in Lorentzian target space, in the presence of a quantized 4-volume form. The Hubble parameter is singular at the BB, and becomes small at late times. There is no singularity from the target space point of view, and the brane is Euclidean "before" the BB. Both recollapsing and expanding universe solutions are obtained, depending on the mass parameters.

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“…[23][24][25][26][27]. The starting point is the Lie algebra so(6) ∼ = su(4), with generators M ab , a, b = 1, .…”

Section: The Euclidean Fuzzy 4-spherementioning

confidence: 99%

Cosmological space-times with resolved Big Bang in Yang-Mills matrix models

Steinacker

2018

J. High Energ. Phys.

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“…This can be done on even-dimensional co-adjoint orbits of Lie groups, which are symplectic manifolds [43,44,45,46,47,48,49,50,51], like the two-sphere S 2 and the CP n complex projective spaces.…”

Section: Introductionmentioning

confidence: 99%

Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere

Panero¹

2006

SIGMA

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Abstract. We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to different commutative or non-commutative spaces. We present some of the theories which have been investigated in this framework, with a particular attention to the scalar model. Then we comment on the results recently obtained from Monte Carlo simulations, and show a preview of new numerical data, which are consistent with the expected transition between two phases characterised by the topology of the support of a matrix eigenvalue distribution.

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“…After an analysis of the representation content for (2.6) it was proved in [6] that ∆ I is a strictly positive operator for the non-S 4 F modes and has as its kernel precisely the S 4 F modes. The mechanism is one of probabilistic penalization as the probability of a field configuration Φ can be separated into…”

Section: F Revisitedmentioning

confidence: 99%

“…The parameter R is a length scale that fixes the size of CP N . We will analize in what follows a deformation of the Laplacian which breaks the round symmetry and corresponds to a Kaluza-Klein-type [13] fuzzy space, first constructed in [6], which effectively reduces a scalar field theory from CP 3 F to S 4 F through a probabilistic penalization method. To this end we shall briefly review the construction of S 4 F .…”

Section: Contents 1 Introductionmentioning

confidence: 99%