scholarly journals Quantization of emergent gravity

2015 ◽  
Vol 30 (04n05) ◽  
pp. 1550016 ◽  
Author(s):  
Hyun Seok Yang
Keyword(s):  
Gauge Theory ◽  
Quantum Gravity ◽  
Equivalence Principle ◽  
Symplectic Geometry ◽  
Symplectic Structure ◽  
Space Time ◽  
Quantization Scheme ◽  
Emergent Gravity ◽  
Darboux Theorem ◽  
Matter Fields

Emergent gravity is based on a novel form of the equivalence principle known as the Darboux theorem or the Moser lemma in symplectic geometry stating that the electromagnetic force can always be eliminated by a local coordinate transformation as far as space–time admits a symplectic structure, in other words, a microscopic space–time becomes noncommutative (NC). If gravity emerges from U(1) gauge theory on NC space–time, this picture of emergent gravity suggests a completely new quantization scheme where quantum gravity is defined by quantizing space–time itself, leading to a dynamical NC space–time. Therefore the quantization of emergent gravity is radically different from the conventional approach trying to quantize a phase space of metric fields. This approach for quantum gravity allows a background-independent formulation where space–time and matter fields are equally emergent from a universal vacuum of quantum gravity.

scholarly journals EMERGENT GEOMETRY AND QUANTUM GRAVITY

2010 ◽  
Vol 25 (28) ◽  
pp. 2381-2397 ◽  
Author(s):  
HYUN SEOK YANG
Keyword(s):  
Quantum Gravity ◽  
Symplectic Geometry ◽  
Symplectic Structure ◽  
Gravitational Constant ◽  
Planck Scale ◽  
Riemannian Metric ◽  
Natural Unit ◽  
Emergent Geometry ◽  
Noncommutative Spacetime ◽  
Matter Fields

We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant [Formula: see text] whose physical dimension is of (length)2 in natural unit introduces a symplectic structure of spacetime which causes a noncommutative spacetime at the Planck scale L P . The symplectic structure of spacetime M leads to an isomorphism between symplectic geometry (M, ω) and Riemannian geometry (M, g) where the deformations of symplectic structure ω in terms of electromagnetic fields F = dA are transformed into those of Riemannian metric g. This approach for quantum gravity allows a background independent formulation where spacetime as well as matter fields is equally emergent from a universal vacuum of quantum gravity which is thus dubbed as the quantum equivalence principle.

scholarly journals DARK ENERGY AND EMERGENT SPACETIME

2011 ◽  
Vol 01 ◽  
pp. 266-271
Author(s):  
HYUN SEOK YANG
Keyword(s):  
Dark Energy ◽  
Symplectic Geometry ◽  
Cosmological Constant Problem ◽  
Geometric Framework ◽  
Emergent Gravity ◽  
Flat Spacetime ◽  
Darboux Theorem ◽  
Noncommutative Spacetime ◽  
Emergent Spacetime ◽  
Planck Energy

A natural geometric framework of noncommutative spacetime is symplectic geometry rather than Riemannian geometry. The Darboux theorem in symplectic geometry then admits a novel form of the equivalence principle such that the electromagnetism in noncommutative spacetime can be regarded as a theory of gravity. Remarkably the emergent gravity reveals a noble picture about the origin of spacetime, dubbed as emergent spacetime, which is radically different from any previous physical theory all of which describe what happens in a given spacetime. In particular, the emergent gravity naturally explains the dynamical origin of flat spacetime, which is absent in Einstein gravity: A flat spacetime is not free gratis but a result of Planck energy condensation in a vacuum. This emergent spacetime picture, if it is correct anyway, turns out to be essential to resolve the cosmological constant problem, to understand the nature of dark energy and to explain why gravity is so weak compared to other forces.

scholarly journals Loop Quantum Black Hole Extensions Within the Improved Dynamics

2021 ◽  
Vol 8 ◽  
Author(s):  
Rodolfo Gambini ◽  
Javier Olmedo ◽  
Jorge Pullin
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Space Time ◽  
Anisotropic Fluid ◽  
Spherically Symmetric ◽  
Quantization Scheme ◽  
White Hole ◽  
Quantum Black Hole ◽  
Black Hole Singularity

We continue our investigation of an improved quantization scheme for spherically symmetric loop quantum gravity. We find that in the region where the black hole singularity appears in the classical theory, the quantum theory contains semi-classical states that approximate general relativity coupled to an effective anisotropic fluid. The singularity is eliminated and the space-time can be continued into a white hole space-time. This is similar to previously considered scenarios based on a loop quantum gravity quantization.

scholarly journals EMERGENT GRAVITY FROM NONCOMMUTATIVE SPACE–TIME

2009 ◽  
Vol 24 (24) ◽  
pp. 4473-4517 ◽  
Author(s):  
HYUN SEOK YANG
Keyword(s):  
Twistor Space ◽  
Complex Geometry ◽  
Space Time ◽  
Noncommutative Space ◽  
Gauge Fields ◽  
Emergent Gravity ◽  
Fuzzy Space ◽  
Higher Order Gravity ◽  
Collective Phenomenon ◽  
Darboux Theorem

We showed before that self-dual electromagnetism in noncommutative (NC) space–time is equivalent to self-dual Einstein gravity. This result implies a striking picture about gravity: gravity can emerge from electromagnetism in NC space–time. Gravity is then a collective phenomenon emerging from gauge fields living in fuzzy space–time. We elucidate in some detail why electromagnetism in NC space–time should be a theory of gravity. In particular, we show that NC electromagnetism is realized through the Darboux theorem as a diffeomorphism symmetry G which is spontaneously broken to symplectomorphism H due to a background symplectic two-form Bμν = (1/θ)μν, giving rise to NC space–time. This leads to a natural speculation that the emergent gravity from NC electromagnetism corresponds to a nonlinear realization G/H of the diffeomorphism group, more generally its NC deformation. We also find some evidences that the emergent gravity contains the structures of generalized complex geometry and NC gravity. To illuminate the emergent gravity, we illustrate how self-dual NC electromagnetism nicely fits with the twistor space describing curved self-dual space–time. We also discuss derivative corrections of Seiberg–Witten map which give rise to higher-order gravity.

scholarly journals Graviton loop contribution to Higgs potential in gauge-Higgs unification

2020 ◽  
Author(s):  
Yasunari Nishikawa
Keyword(s):  
Gauge Theory ◽  
Higgs Boson ◽  
Quantum Gravity ◽  
Gauge Field ◽  
Effective Potential ◽  
Dimensional Space ◽  
Space Time ◽  
Higgs Potential ◽  
Loop Contribution ◽  
Dimensional Space Time

Abstract We study a two-loop finiteness of an effective potential for a Higgs boson that is the fifth component of a gauge field in an U(1) gauge theory coupled to quantum gravity on the five-dimensional space-time M4 × S1. There are two types of diagrams including quantum gravitational corrections. We find that only one type of diagram contributes to the effective potential for the Higgs boson in fact and its magnitude is finite.

scholarly journals SPACE–TIME FOAM MAY VIOLATE THE PRINCIPLE OF EQUIVALENCE

2004 ◽  
Vol 19 (26) ◽  
pp. 4413-4430 ◽  
Author(s):  
JOHN ELLIS ◽  
NICK E. MAVROMATOS ◽  
DIMITRI V. NANOPOULOS ◽  
ALEXANDER S. SAKHAROV
Keyword(s):  
Quantum Gravity ◽  
Equivalence Principle ◽  
Lorentz Invariance ◽  
Charged Particles ◽  
Energetic Particles ◽  
Space Time ◽  
Principle Of Equivalence ◽  
Brane Model ◽  
Different Types ◽  
Higher Genus

The interactions of different particle species with the foamy space–time fluctuations expected in quantum gravity theories may not be universal, in which case different types of energetic particles may violate Lorentz invariance by varying amounts, violating the equivalence principle. We illustrate this possibility in two different models of space–time foam based on D-particle fluctuations in either flat Minkowski space or a stack of intersecting D-branes. Both models suggest that Lorentz invariance could be violated for energetic particles that do not carry conserved charges, such as photons, whereas charged particles such electrons would propagate in a Lorentz-inavariant way. The D-brane model further suggests that gluon propagation might violate Lorentz invariance, but not neutrinos. We argue that these conclusions hold at both the tree (lowest-genus) and loop (higher-genus) levels, and discuss their implications for the phenomenology of quantum gravity.

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

scholarly journals Boundary electromagnetic duality from homological edge modes

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Philippe Mathieu ◽  
Nicholas Teh
Keyword(s):  
Gauge Theory ◽  
Symplectic Structure ◽  
Central Charge ◽  
Wilson Line ◽  
Boundary Term ◽  
Global Symmetry ◽  
Homotopy Pullback ◽  
Line Singularities ◽  
Topological Boundary

Abstract Recent years have seen a renewed interest in using ‘edge modes’ to extend the pre-symplectic structure of gauge theory on manifolds with boundaries. Here we further the investigation undertaken in [1] by using the formalism of homotopy pullback and Deligne- Beilinson cohomology to describe an electromagnetic (EM) duality on the boundary of M = B3 × ℝ. Upon breaking a generalized global symmetry, the duality is implemented by a BF-like topological boundary term. We then introduce Wilson line singularities on ∂M and show that these induce the existence of dual edge modes, which we identify as connections over a (−1)-gerbe. We derive the pre-symplectic structure that yields the central charge in [1] and show that the central charge is related to a non-trivial class of the (−1)-gerbe.

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