The fuzzy 4-hyperboloid <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msubsup></mml:math> and higher-spin in Yang–Mills matrix models

Sperling, Marcus; Steinacker, Harold

doi:10.1016/j.nuclphysb.2019.02.027

Cited by 36 publications

(75 citation statements)

References 66 publications

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“…Note that (5.26) has a cutoff at spin s = n, which results from the fact that the fiber on fuzzy CP 1,2 is really a fuzzy sphere S 2 n , which supports only harmonics up to spin n. This is discussed briefly below (5.15) and shown in detail in [18]. This cutoff disappears in the semi-classical limit, where the C s are modules over C 0 ∼ = C(H 4 ), interpreted as sections of higher spin bundles over H 4 .…”

Section: Algebraic Descriptionmentioning

confidence: 96%

“…Semi-classical structure. In the semi-classical limit, the generators x µ and t µ satisfy the following constraints [18] x…”

Section: Algebraic Descriptionmentioning

confidence: 99%

“…In particular, C (s,0) ⊂ C s is the space of divergence-free traceless space-like rank s tensor fields on M 3,1 , in radiation gauge. We can then organize the C s modes into primals and descendants [18,20]…”

Section: Algebra Of Functions and Higher-spinmentioning

confidence: 99%

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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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Section: Algebraic Descriptionmentioning

confidence: 96%

“…Semi-classical structure. In the semi-classical limit, the generators x µ and t µ satisfy the following constraints [18] x…”

Section: Algebraic Descriptionmentioning

confidence: 99%

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

Steinacker

2020

Class. Quantum Grav.

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“…As a vector space, the constraints including (2.7) encode the degrees of freedom 8 a hs-algebra in 4 dimensions at each point on M; for more details see e.g. section 4 in [31]. There are hence 2 different points of view of the present structure.…”

Section: Bundle Structure and Higher-spin Fields As Push-forwardsmentioning

confidence: 99%

Higher-spin gravity and torsion on quantized space-time in matrix models

Steinacker

2020

J. High Energ. Phys.

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A geometric formalism is developed which allows to describe the non-linear regime of higher-spin gravity emerging on a cosmological quantum space-time in the IKKT matrix model. The vacuum solutions are Ricci-flat up to an effective vacuum energy-momentum tensor quadratic in the torsion, which arises from a Weitzenböck-type higher spin connection. Torsion is expected to be significant only at cosmic scales and around very massive objects, and could behave like dark matter. A non-linear equation for the torsion tensor is found, which encodes the Yang-Mills equations of the matrix model. The metric and torsion transform covariantly under a higher-spin generalization of volume-preserving diffeomorphisms, which arises from the gauge invariance of the matrix model. known as UV/IR mixing [2][3][4]. They cancel only in the maximally supersymmetric IKKT matrix model [5], which should thus have the best chance to describe physics, leading to an unexpected link with string theory. However, it is not obvious how to obtain gravity from Yang-Mills-type matrix models such as the IKKT model. There are intriguing hints such as non-local gauge transformations and Ricci-flat propagating metric fluctuations [6][7][8], but the presence of an anti-symmetric tensor θ µν in space-time leads to a dangerous breaking of Lorentz invariance. This problem can be overcome by considering a higher-spin generalization, where θ µν is replaced by a twisted bundle of such tensors over space-time. This is realized in a simple solution of the IKKT model with a mass term interpreted as cosmological FLRW space-time M, based on the doubleton representations of so(4, 2) [9, 10], cf. [11]. It leads to a higher spin gauge theory which is invariant under a higher spin generalization of volume-preserving diffeomorphisms, ghost-free at the linearized level, and includes spin 2 gravitons. A linearized Schwarzschild-like solution was also found [12]. The theory has intriguing structural similarities with Vasilievs higherspin gravity [13,14], but also crucial differences 2 : it is defined through an action, both IR and UV scale parameters are present, and there are 5 propagating metric modes which could be interpreted as "would-be massive" gravitons. In the present paper, we study that higher-spin theory at the non-linear level. This is not straightforward because the model is of Yang-Mills type, there is no Einstein-Hilbert action, and everything is based on Poisson brackets (or commutators). The gauge symmetry corresponds to generalized diffeomorphisms rather than local Lorentz transformations 3 , hence it is not some reformulation of GR in the spirit of MacDowell-Mansouri [23]. A more appropriate approach can be found in a paper by Langmann and Szabo (LS) [24], who pointed out that a dimensional reduction of a gauge theory in 8-dimensional phase space with suitable constraints can be interpreted in terms of 4-dimensional teleparallel gravity through torsion. Although their setup does not provide a complete theory, a similar strategy provides a geometric unders...

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“…As it is well-known, this representation is not unitary but it may be used to induce the UIR that we are seeking for. To do so, we introduce a four component spinor of the form [42][43][44]…”

Section: )mentioning

confidence: 99%

Extended dynamical symmetries of Landau levels in higher dimensions

Kürkçüoğlu

Ünal

Yurdusen

2020

J. High Energ. Phys.

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Continuum models for time-reversal (TR) invariant topological insulators (TIs) in d ≥ 3 dimensions are provided by harmonic oscillators coupled to certain SO(d) gauge fields. These models are equivalent to the presence of spin-orbit (SO) interaction in the oscillator Hamiltonians at a critical coupling strength (equivalent to the harmonic oscillator frequency) and leads to flat Landau Level (LL) spectra and therefore to infinite degeneracy of either the positive or the negative helicity states depending on the sign of the SO coupling. Generalizing the results of [1] to d ≥ 4, we construct vector operators commuting with these Hamiltonians and show that SO(d, 2) emerges as the non-compact extended dynamical symmetry. Focusing on the model in four dimensions, we demonstrate that the infinite degeneracy of the flat spectra can be fully explained in terms of the discrete unitary representations of SO(4, 2), i.e. the doubletons. The degeneracy in the opposite helicity branch is finite, but can still be explained exploiting the complex conjugate doubleton representations. Subsequently, the analysis is generalized to d dimensions, distinguishing the cases of odd and even d. We also determine the spectrum generating algebra in these models and briefly comment on the algebraic organization of the LL states w.r.t to an underlying "deformed" AdS geometry as well as on the organization of the surface states under open boundary conditions in view of our results.

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The fuzzy 4-hyperboloid Hn4 and higher-spin in Yang–Mills matrix models

Cited by 36 publications

References 66 publications

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

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

Higher-spin gravity and torsion on quantized space-time in matrix models

Extended dynamical symmetries of Landau levels in higher dimensions

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