Three-dimensional gravity as a noncommutative gauge theory

Manolakos, G.; Manousselis, P.; Zoupanos, George

doi:10.22323/1.347.0096

Cited by 4 publications

(3 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Covariant higher-dimensional fuzzy spaces were studied e.g. in [2,4,6,54,[88][89][90][91][92][93][94][95], which are similar in spirit to Snyder space [41,96], see also [47] for a somewhat related ansatz. In particular, the relation of fuzzy S 4 to fuzzy CP 2 was pointed out in [5,97,98], which is analogous to the bundle structure discussed in section 5.…”

Section: Further Literaturementioning

confidence: 99%

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

Steinacker

2020

Class. Quantum Grav.

View full text Add to dashboard Cite

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.

show abstract

Section: Further Literaturementioning

confidence: 99%

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

Steinacker

2020

Class. Quantum Grav.

View full text Add to dashboard Cite

show abstract

“…Next, aiming at the construction of a 4-dim noncommutative gravity model, we first got involved with the construction of a 4-dim covariant noncommutative space that would serve as the background space on which the gauge theory would be constructed [71] (see also [72]). Motivated by refs [51][52][53], we focused on the construction of a covariant fuzzy version of the 4-dim de Sitter space and obtained the defining commutation relation of its coordinates.…”

Section: Introductionmentioning

confidence: 99%

Four‐Dimensional Gravity on a Covariant Noncommutative Space (II)

Manolakos

Manousselis

Zoupanos

2021

Fortschritte der Physik

View full text Add to dashboard Cite

Based on the construction of the 4‐dim noncommutative gravity model described in our previous work, first, a more extended description of the covariant noncommutative space (fuzzy 4‐dim de Sitter space), which accommodates the gravity model, is presented and then the corresponding field equations, which are obtained after variation of the previously proposed action, are extracted. Also, a spontaneous breaking of the initial symmetry is performed, this time induced by the introduction of an auxiliary scalar field, and its implications in the reduced theory, which is produced after considering the commutative limit, are examined.

show abstract

“…The tensor fields are accordingly characterized by the transformation under the local SO(3) stabilizer group, and the term "scalar modes" is understood in this sense throughout 1 It is well-known that gravity can be obtained from a Yang-Mills-type action by imposing constraints, cf. [11][12][13]. However this essentially amounts to a reformulation of classical GR, and the usual problems are expected to arise upon quantization.…”

mentioning

confidence: 99%

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

Steinacker

2019

Class. Quantum Grav.

View full text Add to dashboard Cite

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.Since the notorious problems in attempts to quantize gravity arise primarily from the Einstein-Hilbert action, is is very desirable to find another framework for gravity, which is more suitable for quantization. String theory provides such a framework, but the traditional approach using compactifications leads to a host of issues, notably lack of predictivity. This suggests to use matrix models as a starting point, and in particular the IKKT or IIB model [2], which was originally proposed as a constructive definition of string theory. Remarkably, numerical studies in this nonperturbative formulation provide evidence [3-5] that 3+1-dimensional configurations arise at the non-perturbative level, tentatively interpreted as expanding universe. However, this requires a new mechanism for gravity on 3+1-dimensional non-commutative backgrounds as in [1], which does not rely on compactification. The present paper provides further evidence and insights for this mechanism. The (linearized) Schwarzschild metric is clearly the benchmark for any viable theory of gravity. There has been considerable effort to find noncommutative analogs of the Schwarzschild metric from various approaches, leading to a number of proposals [6-9] and references therein, cf. also [10]; however, none is truly satisfactory. The proposals are typically obtained by some ad-hoc modification of the classical solution, without any intrinsic role of noncommutativity, which is put in by hand. In contrast, the quantum structure (or its semi-classical limit) plays a central role in the present framework. Our solution is a deformation of the noncommutative background which respects an exact SO(3) rotation symmetry, even though there are only finitely many d.o.f. per unit volume. The solution has a good asymptotics at large distances, allowing superpositions corresponding to arbitrary mass distributions. In fact we obtain generic quasi-static Ricci-flat linearized perturbations, which complement the Ricci-flat propagating gravitons found in [1]. This realization of the (linearized) Schwarzschild solution is remarkable and may seem surprising, because the action is of Yang-Mills type, and no Einstein-Hilbert-like action is required 1 . This means that the theory has a good chance to survive upon quantization, which is naturally defined via integration over the s...

show abstract

Three-dimensional gravity as a noncommutative gauge theory

Cited by 4 publications

References 60 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

Four‐Dimensional Gravity on a Covariant Noncommutative Space (II)

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

Contact Info

Product

Resources

About