arXiv subjects

Harold C. Steinacker

Publications and source records attributed to Harold C. Steinacker.

At least 37 records · Page 2Linked to original sources

arXiv2023

Cosmic time evolution and propagator from a Yang-Mills matrix model

We consider a solution of a IKKT-type matrix model which can be considered as a 1+1-dimensional space-time with Minkowski signature and a Big Bounce-like singularity. A suitable $i\varepsilon$ regularization of the Lorentzian matrix integral is proposed, which leads to the standard $i\varepsilon$-prescription for the effective field theory. In particular, the Feynman propagator is recovered locally for late times. This demonstrates that a causal structure and time evolution can emerge in the matrix model, even on non-trivial geometries. We also consider the propagation of modes through the Big Bounce, and observe an interesting correlation between the post-BB and pre-BB sheets, which reflects the structure of the brane in target space.

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arXiv2023

One-loop effective action and emergent gravity on quantum spaces in the IKKT matrix model

A detailed derivation of $3+1$ dimensional induced or emergent gravity in the IKKT matrix model at one loop is given, as announced in [1]. The mechanism requires a brane configuration with structure ${\cal M}^{3,1}\times {\cal K} \subset {\mathbb R}^{9,1}$, where ${\cal M}^{3,1}$ is the noncommutative space-time brane, and ${\cal K}$ are compact fuzzy extra dimensions embedded in target space. The 3+1-dimensional Einstein-Hilbert action then arises in the one loop effective action of the maximally supersymmetric IIB or IKKT matrix model, with effective Newton constant determined by the Kaluza-Klein scale of ${\cal K}$. At weak coupling, all physical modes are confined to the brane, leading to $3+1$-dimensional low-energy physics. The Einstein-Hilbert action can be interpreted as interaction of ${\cal K}$ with the space-time brane via IIB supergravity. The vacuum energy does not act as cosmological constant, but stabilizes the brane structure at one loop.

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arXiv2023

Exploring the gravity sector of emergent higher-spin gravity: effective action and a solution

We elaborate the description of the semi-classical gravity sector of Yang-Mills matrix models on a covariant quantum FLRW background. The basic geometric structure is a frame, which arises from the Poisson structure on an underlying $S^2$ bundle over space-time. The equations of motion for the associated Weitzenböck torsion obtained in arXiv:2002.02742 are rewritten in the form of Yang-Mills-type equations for the frame. An effective action is found which reproduces these equations of motion, which contains an Einstein-Hilbert term coupled to a dilaton, an axion and a Maxwell-type term for the dynamical frame. An explicit rotationally invariant solution is found, which describes a gravitational field coupled to the dilaton.

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arXiv2023

Gravity as a Quantum Effect on Quantum Space-Time

The 3+1-dimensional Einstein-Hilbert action is obtained from the 1-loop effective action on noncommutative branes in the IIB or IKKT matrix model. The presence of compact fuzzy extra dimensions ${\cal K}$ as well as maximal supersymmetry of the model is essential. The E-H action can be interpreted as interaction of ${\cal K}$ with the space-time brane via IIB supergravity, and the effective Newton constant is determined by the Kaluza-Klein scale of ${\cal K}$. The bare matrix model defines a pre-gravity action with 2 derivatives less than the induced E-H action, governing the cosmological regime. The perturbative physics is confined to the space-time brane, which for covariant quantum space-times includes all dof of gravity, as well as a tower of higher-spin modes. The vacuum energy is given in terms of the symplectic volume form, and hence does not act as cosmological constant.

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arXiv2023

Quantum (Matrix) Geometry and Quasi-Coherent States

A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and allows to extract the underlying classical space without requiring the limit of large matrices or representation theory. The approach is based on the previously introduced concept of quasi-coherent states. In particular, a concept of quantum Kähler geometry arises naturally, which includes the well-known quantized coadjoint orbits such as the fuzzy sphere $S^2_N$ and fuzzy $\mathbb{C} P^n_N$. A quantization map for quantum Kähler geometries is established. Some examples of quantum geometries which are not Kähler are identified, including the minimal fuzzy torus.

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arXiv2023

Fermions on curved backgrounds of matrix models

We discuss the propagation of fermions on generic, curved branes in IKKT-type matrix models. The Dirac operator can be understood either in terms of a Weitzenböck connection, or in terms of the Levi-Civita connection with extra torsion term. We discuss in detail the coupling of spin to the background geometry using the JWKB approximation. Despite the absence of local Lorentz invariance in the underlying IKKT framework, our results agree with the expectations of Einstein-Cartan theory, and differ from general relativity only by an extra coupling to the totally antisymmetric part of the torsion. The case of FLRW cosmic background solutions is discussed as a special case.

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arXiv2022

On the propagation across the big bounce in an open quantum FLRW cosmology

The propagation of a scalar field in an open FLRW bounce-type quantum spacetime is examined, which arises within the framework of the IKKT matrix theory. In the first part of the paper, we employ general-relativity tools to study null and timelike geodesics at the classical level. This analysis reveals that massless and massive non-interacting particles can travel across the big bounce. We then exploit quantum-field-theory techniques to evaluate the scalar field propagator. In the late-time regime, we find that it resembles the standard Feynman propagator of flat Minkowski space, whereas for early times it governs the propagation across the big bounce and gives rise to a well-defined correlation between two points on opposite sheets of the spacetime.

gr-qc↗

arXiv2022

Classical space-time geometry in the IKKT matrix model

We discuss the reconstruction of generic 3+1-dimensional space-time geometries from covariant quantum spaces as backgrounds in the IKKT matrix model. An explicit recipe to realize generic classical geometries is provided. Even though this typically entails some higher-spin contributions, these do not significantly modify the physical content of the model in the weak gravity regime. This justifies the framework for emergent gravity given by the semi-classical matrix model, supplemented by an induced Einstein-Hilbert action which arises in the presence of fuzzy extra dimensions.

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arXiv2022

String modes, propagators and loops on fuzzy spaces

We present a systematic organization of functions and operators on the fuzzy 2-sphere in terms of string modes, which are optimally localized in position and momentum space. This allows to separate the semi-classical and the deep quantum regime of non-commutative quantum field theory and exhibits its nonlocal nature. This organization greatly simplifies the computation of loop contributions, avoiding oscillatory integrals and providing the effective action directly in position space. UV/IR mixing is understood as nonlocality arising from long string modes in the loops. The method is suited for any quantized symplectic space.

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arXiv2021

Spherically symmetric solutions of higher-spin gravity in the IKKT matrix model

We present a systematic study of spherically symmetric vacuum solutions of the IKKT matrix model, within the framework of semi-classical covariant quantum geometries. All asymptotically flat solutions of the equations of motion of the frame are found explicitly. They reproduce the linearized Schwarzschild geometry for large $r$ but deviate from it at the non-linear level, and include contributions from dilaton and axion. They are pertinent to the pre-gravity theory arising on classical brane solutions within the classical matrix model, before taking into account the Einstein-Hilbert term induced by quantum effects. We also address the problem of reconstructing matrix configurations corresponding to some given frame, and show that this problem can always be solved at the geometrical level of the underlying higher spin theory, ignoring possible higher spin modes.

hep-th↗

arXiv2021

Higher-spin kinematics & no ghosts on quantum space-time in Yang-Mills matrix models

A classification of bosonic on- and off-shell modes on a cosmological quantum space-time solution of the IIB matrix model is given, which leads to a higher-spin gauge theory. In particular, the no-ghost-theorem is established. The physical on-shell modes consist of 2 towers of higher-spin modes, which are effectively massless but include would-be massive degrees of freedom. The off-shell modes consist of 4 towers of higher-spin modes, one of which was missing previously. The noncommutativity leads to a cutoff in spin, which disappears in the semi-classical limit. An explicit basis allows to obtain the full propagator, which is governed by a universal effective metric. The physical metric fluctuations arise from would-be massive spin 2 modes, which were previously shown to include the linearized Schwarzschild solution. Due to the relation with ${\cal N}=4$ super-Yang-Mills, this is expected to define a consistent quantum theory in 3+1 dimensions, which includes gravity.

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arXiv2020

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

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.

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arXiv2020

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

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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arXiv2019

Scalar modes and the linearized Schwarzschild solution on a quantized FLRW space-time in Yang-Mills matrix models

We study scalar perturbations of a recently found 3+1-dimensional FLRW quantum space-time solution in Yang-Mills matrix models. In particular, the linearized Schwarzschild metric is obtained as a solution. It arises from a quasi-static would-be massive graviton mode, and slowly decreases during the cosmic expansion. Along with the propagating graviton modes, this strongly suggests that 3+1 dimensional (quantum) gravity emerges from the IKKT matrix model on this background. For the dynamical scalar modes, non-linear effects must be taken into account. We argue that they lead to non-Ricci-flat metric perturbations with very long wavelengths, which would be perceived as dark matter from the GR point of view.

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arXiv2018

Quantized open FRW cosmology from Yang-Mills matrix models

We present simple solutions of IKKT-type matrix models describing a quantized homogeneous and isotropic cosmology with $k=-1$, finite density of microstates and a resolved Big Bang. At late times, a linear coasting cosmology $a(t) \propto t$ is obtained, which is remarkably close to observation. The solution consists of two sheets with opposite intrinsic chiralities, which are connected in a Euclidean pre-big bang era.

hep-th↗

arXiv2018

Intersecting branes, Higgs sector, and chirality from $\mathcal{N}=4$ SYM with soft SUSY breaking

We consider $SU(N)$ $\mathcal{N}=4$ super Yang-Mills with cubic and quadratic soft SUSY breaking potential, such that the global $SU(4)_R$ is broken to $SU(3)$ or further. As shown recently, this set-up supports a rich set of non-trivial vacua with the geometry of self-intersecting $SU(3)$ branes in 6 extra dimensions. The zero modes on these branes can be interpreted as 3 generations of bosonic and chiral fermionic strings connecting the branes at their intersections. Here, we uncover a large class of exact solutions consisting of branes connected by Higgs condensates, leading to Yukawa couplings between the chiral fermionic zero modes. Under certain decoupling conditions, the backreaction of the Higgs on the branes vanishes exactly. The resulting physics is that of a spontaneously broken chiral gauge theory on branes with fluxes. In particular, we identify combined brane plus Higgs configurations which lead to gauge fields that couple to chiral fermions at low energy. This turns out to be quite close to the Standard Model and its constructions via branes in string theory. As a by-product, we construct a $G_2$-brane solution corresponding to a squashed fuzzy coadjoint orbit of $G_2$.

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arXiv2018

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

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.

hep-th↗

arXiv2017

Higher spin gauge theory on fuzzy $S^4_N$

We examine in detail the higher spin fields which arise on the basic fuzzy sphere $S^4_N$ in the semi-classical limit. The space of functions can be identified with functions on classical $S^4$ taking values in a higher spin algebra associated to $\mathfrak{so}(5)$. We derive an explicit and complete classification of the scalars and one-forms on the semi-classical limit of $S_N^4$. The resulting kinematics is reminiscent of Vasiliev theory. Yang-Mills matrix models naturally provide an action formulation for higher spin gauge theory on $S^4$, with 4 irreducible modes for each spin $s\geq 1$. We diagonalize the quadratic part of the effective action and exactly evaluate the quadratic part in the spin 2 sector. By identifying the linear perturbation of the effective metric, we obtain the exact kinetic term for all graviton candidates. At the classical level, matter $T_{μν}$ leads to three different contributions to the linearized metric: one consistent with linearized GR, one more rapidly decreasing contribution, and one non-propagating contribution localized at $T_{μν}$. The latter is too large to be physically acceptable, unless there is a significant induced quantum action. This issue should be resolved on generalized fuzzy spaces.

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