Narrow Results

In this brief review, we summarize the new development on the correspondence between noncommutative (NC) field theory and gravity, shortly referred to as the NCFT/Gravity correspondence. We elucidate why a gauge theory in NC spacetime should be a theory of gravity. A basic reason for the NCFT/Gravity correspondence is that the Λ-symmetry (or B-field transformations) in NC spacetime can be considered as a par with diffeomorphisms, which results from the Darboux theorem. This fact leads to a striking picture about gravity: Gravity can emerge from a gauge theory in NC spacetime. Gravity is then a collective phenomenon emerging from gauge fields living in fuzzy spacetime.

We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant 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.

If the information transfer between test particle and holographic screen in entropic gravity respects both the uncertainty principle and causality, a lower limit on the number of bits in the universe relative to its mass may be derived. Furthermore, these limits indicate particles that putatively travel at the speed of light — the photon and/or graviton — have a nonzero mass m ≥10^-68kg. This result is found to be in excellent agreement with current experimental mass bounds on the graviton and photon, suggesting that entropic gravity may be the result of a (recent) softly-broken local symmetry. Stronger bounds emerge from consideration of ultradense matter such as neutron stars, yielding limits of m ≥10^-48–10^-50kg, barely within the experimental photon range and outside that of the graviton. We find that for black holes these criteria cannot be satisfied, and suggest some possible implications of this result.

The entropic formulation of the inertia and the gravity relies on quantum, geometrical and informational arguments. The fact that the results are completely classical is misleading. In this paper, we argue that the entropic formulation provides new insights into the quantum nature of the inertia and the gravity. We use the entropic postulate to determine the quantum uncertainty in the law of inertia and in the law of gravity in the Newtonian Mechanics, the Special Relativity and in the General Relativity. These results are obtained by considering the most general quantum property of the matter represented by the Uncertainty Principle and by postulating an expression for the uncertainty of the entropy such that: (i) it is the simplest quantum generalization of the postulate of the variation of the entropy and (ii) it reduces to the variation of the entropy in the absence of the uncertainty.

Research during the last one decade or so suggests that the gravitational field equations in a large class of theories (including, but not limited to, general relativity) have the same status as the equations of, say, gas dynamics or elasticity. This paradigm provides a refreshingly different way of interpreting spacetime dynamics and highlights the fact that several features of classical gravitational theories have direct thermodynamic interpretation. I review the recent progress in this approach, achieved during the last few years.

We review some recent works by Carone, Erlich and Vaman on composite gravitons in metric-independent quantum field theories, with the aim of clarifying a number of basic issues. Focusing on a theory of scalar fields presented previously in the literature, we clarify the meaning of the tunings required to obtain a massless graviton. We argue that this formulation can be interpreted as the massless limit of a theory of massive composite gravitons in which the graviton mass term is not of Pauli–Fierz form. We then suggest closely related theories that can be defined without such a limiting procedure (and hence without worry about possible ghosts). Finally, we comment on the importance of finding a compelling ultraviolet completion for models of this type, and discuss some possibilities.

In the paper arXiv:0706.1618[hep-th], the number distribution of the low-lying spectra around Gaussian solutions representing various dimensional fuzzy tori of a tensor model was numerically shown to be in accordance with the general relativity on tori. In this paper, I perform more detailed numerical analysis of the properties of the modes for two-dimensional fuzzy tori, and obtain conclusive evidences for the agreement. Under a proposed correspondence between the rank-3 tensor in tensor models and the metric tensor in the general relativity, conclusive agreement is obtained between the profiles of the low-lying modes in a tensor model and the metric modes transverse to the general coordinate transformation. Moreover, the low-lying modes are shown to be well on a massless trajectory with quartic momentum dependence in the tensor model. This is in agreement with that the lowest momentum dependence of metric fluctuations in the general relativity will come from the R²-term, since the R-term is topological in two dimensions. These evidences support the idea that the low-lying low-momentum dynamics around the Gaussian solutions of tensor models is described by the general relativity. I also propose a renormalization procedure for tensor models. A classical application of the procedure makes the patterns of the low-lying spectra drastically clearer, and suggests also the existence of massive trajectories.

We consider a statistical model of interacting 4-simplices fluctuating in an N-dimensional target space. We argue that a gravitational theory may arise as a low energy effective theory in a strongly interacting phase where the simplices form clusters with an emergent space and time with the Euclidean signature. In the large N limit, two possible phases are discussed, that is, "gravitational Coulomb phase" and "gravitational Higgs phase."

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 B_μν = (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.

We investigate some of the quantum gravity effects on a vacuum created pair of -brane by a nonlinear U(1) gauge theory on a D₄-brane. In particular, we obtain a four-dimensional quantum Kerr–(Newman) black hole in an effective torsion curvature formalism sourced by a two form dynamics in the worldvolume of a D₄-brane on S¹. Interestingly, the event horizon is found to be independent of a nonlinear electric charge and the 4D quantum black hole is shown to describe degenerate vacua in string theory. We show that the quantum Kerr brane universe possesses its origin in a de Sitter vacuum. In a nearly S₂-symmetric limit, the Kerr geometries may seen to describe a Schwarzschild and Reissner–Nordstrom quantum black holes. It is argued that a quantum Reissner–Nordstrom tunnels to a large class of degenerate Schwarzschild vacua. In a low energy limit, the nonlinear electric charge becomes significant at the expense of the degeneracies. In the limit, the quantum geometries may identify with the semiclassical black holes established in Einstein gravity. Analysis reveals that a quantum geometry on a vacuum created D₃-brane universe may be described by a low energy perturbative string vacuum in presence of a nonperturbative quantum correction.

This is a review of some recent works which demonstrate how the classical equations of gravity in AdS themselves hold the key to understand their holographic origin in the form of a strongly coupled large N QFT whose algebra of local operators can be generated by a few (single-trace) elements. I discuss how this can be realized by reformulating Einstein’s equations in AdS in the form of a nonperturbative RG flow that further leads to a new approach toward constructing strongly interacting QFTs. In particular, the RG flow can self-determine the UV data that are otherwise obtained by solving classical gravity equations and demanding that the solutions do not have naked singularities. For a concrete demonstration, I focus on the hydrodynamic limit in which case this RG flow connects the AdS/CFT correspondence with the membrane paradigm, and also reproduces the known values of the dual QFT transport coefficients.

Informational dependence between statistical or quantum subsystems can be described with Fisher information matrix or Fubini-Study metric obtained from variations/shifts of the sample/configuration space coordinates. Using these (noncovariant) objects as macroscopic constraints, we consider statistical ensembles over the space of classical probability distributions (i.e. in statistical space) or quantum wave functions (i.e. in Hilbert space). The ensembles are covariantized using dual field theories with either complex scalar field (identified with complex wave functions) or real scalar field (identified with square roots of probabilities). We construct space–time ensembles for which an approximate Schrodinger dynamics is satisfied by the dual field (which we call infoton due to its informational origin) and argue that a full space–time covariance on the field theory side is dual to local computations on the information theory side. We define a fully covariant information-computation tensor and show that it must satisfy certain conservation equations.

Then we switch to a thermodynamic description of the quantum/statistical systems and argue that the (inverse of) space–time metric tensor is a conjugate thermodynamic variable to the ensemble-averaged information-computation tensor. In (local) equilibrium, the entropy production vanishes, and the metric is not dynamical, but away from the equilibrium the entropy production gives rise to an emergent dynamics of the metric. This dynamics can be described approximately by expanding the entropy production into products of generalized forces (derivatives of metric) and conjugate fluxes. Near equilibrium, these fluxes are given by an Onsager tensor contracted with generalized forces and on the grounds of time-reversal symmetry, the Onsager tensor is expected to be symmetric. We show that a particularly simple and highly symmetric form of the Onsager tensor gives rise to the Einstein–Hilbert term. This proves that general relativity is equivalent to a theory of nonequilibrium (thermo)dynamics of the metric, but the theory is expected to break down far away from equilibrium where the symmetries of the Onsager tensor are to be broken.

There are strong reasons to believe that the gravitational interaction — described in terms of a metric on a smooth space–time — is an emergent, long wavelength phenomenon, like elasticity. I describe a concrete framework for realizing this paradigm against the backdrop of several recent results. In this perspective, quantum fluctuations of the microscopic degrees of freedom of the space–time lead to residual random displacements of any null surface. The latter can be described in terms of an effective theory using an action associated with the normal displacements of the null surfaces. Extremizing this action leads to an equation determining the background geometry. The resulting theory is Einstein gravity at the lowest order with the Lanczos–Lovelock type quantum corrections. The metric is not a dynamical variable in this approach and gravity arises as a coarse-grained statistical feature of an underlying microscopic theory.

Just as the thermal properties of normal matter demands the existence of microscopic degrees of freedom, the thermal properties of null surfaces — perceived as local Rindler horizons by accelerated observers — demands the existence of microscopic degrees of freedom to spacetime. The distortion of the null surfaces, just like the deformation of an elastic solid, costs entropy. I show how, just like in the case of an elastic solid, one can describe the dynamics of the spacetime solid by introducing an entropy density to the distortion of null surfaces in the spacetime.

Observations indicate that our universe is characterized by a late-time accelerating phase, possibly driven by a cosmological constant Λ, with the dimensionless parameter , where L_P = (Għ/c³)^1/2 is the Planck length. In this review, we describe how the emergent gravity paradigm provides a new insight and a possible solution to the cosmological constant problem. After reviewing the necessary background material, we identify the necessary and sufficient conditions for solving the cosmological constant problem. We show that these conditions are naturally satisfied in the emergent gravity paradigm in which (i) the field equations of gravity are invariant under the addition of a constant to the matter Lagrangian and (ii) the cosmological constant appears as an integration constant in the solution. The numerical value of this integration constant can be related to another dimensionless number (called CosMIn) that counts the number of modes inside a Hubble volume that cross the Hubble radius during the radiation and the matter-dominated epochs of the universe. The emergent gravity paradigm suggests that CosMIn has the numerical value 4π, which, in turn, leads to the correct, observed value of the cosmological constant. Further, the emergent gravity paradigm provides an alternative perspective on cosmology and interprets the expansion of the universe itself as a quest towards holographic equipartition. We discuss the implications of this novel and alternate description of cosmology.

I show that in a general, dynamic spacetime, the rate of change of gravitational momentum is related to the difference between the number of bulk and boundary degrees of freedom. All static spacetimes maintain holographic equipartition; i.e. in these spacetimes, the number of degrees of freedom in the boundary is equal to the number of degrees of freedom in the bulk. It is the departure from holographic equipartition that drives the time evolution of the spacetime. This result, which is equivalent to Einstein's equations, provides an elegant, holographic, description of spacetime dynamics.

The kinematical description of gravity, based on the principle of equivalence, is extraordinarily beautiful. In striking contrast, the field equation $G_{ab}=(1/2)T_{ab}$ is conceptually ugly, lacking in simple physical interpretation or even in common ground to describe the left- and right-hand sides. This paper shows how one can develop all of gravity in an elegant manner by recognizing that the gravitational dynamics describes the heating and cooling of spacetime.

From pure Yang–Mills action for the $SL(5,ℝ)$ group in four Euclidean dimensions we obtain a gravity theory in the first order formalism. Besides the Einstein–Hilbert term, the effective gravity has a cosmological constant term, a curvature squared term, a torsion squared term and a matter sector. To obtain such geometrodynamical theory, asymptotic freedom and the Gribov parameter (soft BRST symmetry breaking) are crucial. Particularly, Newton and cosmological constant are related to these parameters and they also run as functions of the energy scale. One-loop computations are performed and the results are interpreted.

We derive the Einstein equation from the condition that every small causal diamond is a variation of a flat empty diamond with the same free conformal energy, as would be expected for a near-equilibrium state. The attractiveness of gravity hinges on the negativity of the absolute temperature of these diamonds, a property we infer from the generalized entropy.

It is possible that both the classical description of spacetime and the rules of quantum field theory emerge from a more-fundamental structure of physical law. Pregeometric frameworks transfer some of the puzzles of quantum gravity to a semiclassical arena where those puzzles pose less of a challenge. However, in order to provide a satisfactory description of quantum gravity, a semiclassical description must emerge and contain in its description a macroscopic spacetime geometry, dynamical matter, and a gravitational interaction consistent with general relativity at long distances. In this essay, we argue that a framework that includes a stochastic origin for quantum field theory can provide both the emergence of classical spacetime and a quantized gravitational interaction.