Notes on emergent gravity

Lee, Sunggeun; Roychowdhury, Raju; Yang, Hyun Seok

doi:10.1007/jhep09(2012)030

Cited by 16 publications

(24 citation statements)

References 74 publications

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“…We are also trying to find out interesting 1+1 dimensional or 2+1 dimensional DH type systems that can be solved using inverse scattering transform and can be studied to uncover several widely known aspects of integrability. Another testing ground could be various scalar flat Kähler metrics namely the LeBrun metric with U (1) isometry that contains Gibbons-Hawking, Real heaven and Burns metric as special limits and were used to test the bottomup approach of emergent gravity [49]. Using monodromy evolving deformation [50] on Plebanski type self dual Einstein equations which are actually the EOM obtained from the 2-dim chiral U (N ) model in the large N limit and studying integrability might clarify some important issues for the test of emergent gravity [51].…”

Section: Discussionmentioning

confidence: 99%

Bianchi-IX, Darboux–Halphen and Chazy–Ramanujan

Chanda

Guha

Roychowdhury

2016

Int. J. Geom. Methods Mod. Phys.

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Bianchi-IX four metrics are SU (2) invariant solutions of vacuum Einstein equation, for which the connection-wise self-dual case describes the Euler Top, while the curvature-wise self-dual case yields the Ricci flat classical Darboux-Halphen system. It is possible to see such a solution exhibiting Ricci flow. The classical Darboux-Halphen system is a special case of the generalized one that arises from a reduction of the self-dual Yang-Mills equation and the solutions to the related homogeneous quadratic differential equations provide the desired metric. A few integrable and near-integrable dynamical systems related to the DarbouxHalphen system and occurring in the study of Bianchi IX gravitational instanton have been listed as well. We explore in details whether self-duality implies integrability.

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Section: Discussionmentioning

confidence: 99%

Bianchi-IX, Darboux–Halphen and Chazy–Ramanujan

Chanda

Guha

Roychowdhury

2016

Int. J. Geom. Methods Mod. Phys.

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“…However, it seems to be difficult to write down Eq. (4.43) as a local form in terms of symplectic U(1) gauge fields [42]. Now we are ready to discuss how the cosmological constant problem can be resolved in emergent gravity.…”

Section: Matrix Model and Quantum Gravitymentioning

confidence: 99%

Quantized Kähler Geometry and Quantum Gravity

Lee

Yang

2018

J. Korean Phys. Soc.

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It has been often observed that Kähler geometry is essentially a U(1) gauge theory whose field strength is identified with the Kähler form. However it has been pursued neither seriously nor deeply. We argue that this remarkable connection between the Kähler geometry and U(1) gauge theory is a missing corner in our understanding of quantum gravity. We show that the Kähler geometry can be described by a U(1) gauge theory on a symplectic manifold with a slight generalization. We derive a natural Poisson algebra associated with the Kähler geometry we have started with. The quantization of the underlying Poisson algebra leads to a noncommutative U(1) gauge theory which arguably describes a quantized Kähler geometry. The Hilbert space representation of quantized Kähler geometry eventually ends in a zero-dimensional matrix model. We then play with the zero-dimensional matrix model to examine how to recover our starting point-Kähler geometry-from the backgroundindependent formulation. The round-trip journey suggests many remarkable pictures for quantum gravity that will open a new perspective to resolve the notorious problems in theoretical physics such as the cosmological constant problem, hierarchy problem, dark energy, dark matter and cosmic inflation. We also discuss how time emerges to generate a Lorentzian spacetime in the context of emergent gravity.

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“…Recently works in emergent gravity [39] aim at constructing a Riemannian geometry from U (1) gauge fields on a noncommutative spacetime. This construction is invertible to find corresponding U (1) gauge fields on a (generalized) Poisson manifold given a metric (M, g).…”

Section: Hyperkähler Structure and The Ky Tensorsmentioning

confidence: 99%

Taub-NUT as Bertrand Spacetime with Magnetic Fields

Chanda¹,

Guha²,

Raju³

2016

JGSP

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Based on symmetries Taub-NUT shares with Bertrand spacetime, we cast it as the latter with magnetic fields. Its nature as a Bianchi-IX gravitational instanton and other related geometrical properties are reviewed. We provide an easy derivation and comparison between the spatial Killing-Yano tensors deduced from first-integrals and the corresponding hyperkähler structures and finally verify the existence of a graded Lie-algebra structure via Schouten-Nijenhuis brackets.

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Notes on emergent gravity

Cited by 16 publications

References 74 publications

Bianchi-IX, Darboux–Halphen and Chazy–Ramanujan

Bianchi-IX, Darboux–Halphen and Chazy–Ramanujan

Quantized Kähler Geometry and Quantum Gravity

Taub-NUT as Bertrand Spacetime with Magnetic Fields

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