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

We solve a multitrace matrix model approximating the real quartic scalar field theory on the fuzzy sphere and obtain its phase diagram. We generalize this method to models with modified kinetic terms and demonstrate its use by investigating models related to the removal of the UV/IR mixing. We show that for the fuzzy sphere a modification of the kinetic part of the action by higher derivative term can change the phase diagram of the theory such that the triple point moves further from the origin.

Section: Asymmetric One-cut To Symmetric Two-cut Transitionmentioning

confidence: 99%

“…Spaces with noncommuting coordinates have been a part of theoretical physics for quite some time. As a fundamental concept [1,2], as an effective description of different phenomena [3,4], or as various solutions and backgrounds in matrix model descriptions of string theory [5,6].…”

Section: Introductionmentioning

confidence: 99%

Second moment fuzzy-field-theory-like matrix models

Šubjaková

Tekel

2020

“…Together, x µ and t µ generate the algebra C ∼ = C ∞ (CP 1,2 ) of functions on a 6-dimensional bundle, which turns out to be CP 1,2 . This is an SO(4, 1)-equivariant bundle over H 4 , which projects onto M. As explained in [9,30] there is an equivariant quantization map…”

Section: )mentioning

confidence: 97%

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

Steinacker

2020

Self Cite

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...

“…We will focus on Yang-Mills theories dimensionally reduced to 0 dimension, to study the dimensional oxidization byĈ. As we will focus on the bosonic sector, it can also be called the Yang-Mills matrix model [19] or the reduced model [6]. More general analysis of the super Yang-Mills theory coupled with adjoint scalars was made in ref.…”

Section: Gauge Theory With Symmetry Algebraĉmentioning

confidence: 99%

Dimensional oxidization on coset space

Harada

Matsuo

et al. 2020

In the matrix model approaches of string/M theories, one starts from a generic symmetry gl(∞) to reproduce the space-time manifold. In this paper, we consider the generalization in which the space-time manifold emerges from a gauge symmetry algebra which is not necessarily gl(∞). We focus on the second nontrivial example after the toroidal compactification, the coset space G/H, and propose a specific infinite-dimensional symmetry which realizes the geometry. It consists of the gauge-algebra valued functions on the coset and Lorentzian generator pairs associated with the isometry. We show that the 0-dimensional gauge theory with the mass and Chern-Simons terms gives the gauge theory on the coset with scalar fields associated with H.