Lectures on Matrix Field Theory

Ydri, Badis

doi:10.1007/978-3-319-46003-1

Cited by 29 publications

(51 citation statements)

References 215 publications

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“…Fuzzy spaces were introduced in [29,30,55], and useful discussions from a field theoretical point of view can be found e.g. in [56][57][58][59]. More mathematical details on quantized symplectic spaces can be found in [60][61][62], and for quantized coadjoint orbits see e.g.…”

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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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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“…Such an action is manufactured either by requiring it manifest 'Langman-Szabo' duality [82] pµ ↔ 2(θ −1 )µν x ν [83,84] or by adding a 1/p • p term to the free Lagrangian [85], the latter of which directly has the interpretation of adding 'somewhere to put the 1/p • p counterterm'. For recent reviews of these and related efforts we refer the reader to [86,87]. It would be interesting to understand fully the extent to which the physics of these schemes agrees with the interpretation of the IR effects as coming from auxiliary fields [37,61].…”

Section: −γmentioning

confidence: 99%

IR dynamics from UV divergences: UV/IR mixing, NCFT, and the hierarchy problem

Craig

Koren

2020

J. High Energ. Phys.

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The persistence of the hierarchy problem points to a violation of effective field theory expectations. A compelling possibility is that this results from a physical breakdown of EFT, which may arise from correlations between ultraviolet (UV) and infrared (IR) physics. To this end, we study noncommutative field theory (NCFT) as a toy model of UV/IR mixing which generates an emergent infrared scale from ultraviolet dynamics. We explore the range of such theories where ultraviolet divergences are transmogrified into infrared scales, focusing particularly on the properties of Yukawa theory, where we identify a new infrared pole accessible in the s-channel of the Lorentzian theory. We further investigate the interplay between UV-finiteness and UV/IR mixing by studying properties of the softly-broken noncommutative Wess-Zumino model as soft terms are varied relative to the cutoff. While the Lorentz violation inherent to noncommutative theories may limit their direct application to the hierarchy problem, these toy models provide general lessons to guide the realization of UV/IR mixing in more realistic theories.

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“…The phase structure is found to contain a stable uniform ordered phase and the triple point can be estimated. See for example chapter 5 of [43] for the detailed solution of a related general class of multitrace matrix models.…”

Section: The Non-pertrubative Phase Diagrammentioning

confidence: 99%

“…Much of the emergent geometry scenarios discussed in the context of matrix field theory [43] is based on the BFSS and the IKKT matrix models and their lower dimensional analogues given by Yang-Mills matrix models. We may also consider mass deformations of these matrix models obtained by adding mass terms such as the extent of space operator and/or the Myers term [27] to the Yang-Mills action, and as a consequence, the emergent geometry becomes a non-trivial space condensate.…”

Section: Introductionmentioning

confidence: 99%

Quantum gravity as a multitrace matrix model

Ydri

Soudani

Rouag

2017

Int. J. Mod. Phys. A

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We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from two dimensions and captures a large class of spaces admiting a finite spectral triple. These multitrace matrix models sustain emergent geometry as well as growing dimensions and topology change.

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Lectures on Matrix Field Theory

Cited by 29 publications

References 215 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

IR dynamics from UV divergences: UV/IR mixing, NCFT, and the hierarchy problem

Quantum gravity as a multitrace matrix model

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