Emergent Spacetimes Research Articles

Quantum quench in c = 1 matrix model and emergent space-times

We consider quantum quench in large-N singlet sector quantum mechanics of a single hermitian matrix in the double scaling limit. The time dependent parameter is the self-coupling of the matrix. We find exact classical solutions of the collective field theory of the eigenvalue density with abrupt and smooth quench profiles which asymptote to constant couplings at early and late times, and with the system initially in its ground state. With adiabatic initial conditions we find that adiabaticity is always broken regardless of the quench speed. In a class of quench profiles the saddle point solution for the collective field diverges at a finite time, and a further time evolution becomes ambiguous. However the underlying matrix model expressed in terms of fermions predict a smooth time evolution across this point. By studying fluctuations around the saddle point solution we interpret the emergent space-times. They generically have spacelike boundaries where the couplings of the fluctuations diverge and the semi-classical description fails. Only for very finely tuned quench profiles, the space-time is normal.

Equivalence of emergent de Sitter spaces from conformal field theory

Recently, two groups have made distinct proposals for a de Sitter space that is emergent from conformal field theory (CFT). The first proposal is that, for two-dimensional holographic CFTs, the kinematic space of geodesics on a spacelike slice of the asymptotically anti-de Sitter bulk is two-dimensional de Sitter space (dS$_2$), with a metric that can be derived from the entanglement entropy of intervals in the CFT. In the second proposal, de Sitter dynamics emerges naturally from the first law of entanglement entropy for perturbations around the vacuum state of CFTs. We provide support for the equivalence of these two emergent spacetimes in the vacuum case and beyond. In particular, we study the kinematic spaces of nontrivial solutions of $3$d gravity, including the BTZ black string, BTZ black hole, and conical singularities. We argue that the resulting spaces are generically globally hyperbolic spacetimes that support dynamics given boundary conditions at future infinity. For the BTZ black string, corresponding to a thermal state of the CFT, we show that both prescriptions lead to an emergent hyperbolic patch of dS$_2$. We offer a general method for relating kinematic space and the auxiliary de Sitter space that is valid in the vacuum and thermal cases.

Old Game, New Rules: Rethinking the Form of Physics

We investigate the modeling capabilities of sets of coupled classical harmonic oscillators (CHO) in the form of a modeling game. The application of the simple but restrictive rules of the game lead to conditions for an isomorphism between Lie-algebras and real Clifford algebras. We show that the correlations between two coupled classical oscillators find their natural description in the Dirac algebra and allow to model aspects of special relativity, inertial motion, electromagnetism and quantum phenomena including spin in one go. The algebraic properties of Hamiltonian motion of low-dimensional systems can generally be related to certain types of interactions and hence to the dimensionality of emergent space-times. We describe the intrinsic connection between phase space volumes of a 2-dimensional oscillator and the Dirac algebra. In this version of a phase space interpretation of quantum mechanics the (components of the) spinor wavefunction in momentum space are abstract canonical coordinates, and the integrals over the squared wave function represents second moments in phase space. The wave function in ordinary space-time can be obtained via Fourier transformation. Within this modeling game, 3+1-dimensional space-time is interpreted as a structural property of electromagnetic interaction. A generalization selects a series of Clifford algebras of specific dimensions with similar properties, specifically also 10- and 26-dimensional real Clifford algebras.

Covariant quantum fields on noncommutative spacetimes

A spinless covariant field $\phi$ on Minkowski spacetime $\M^{d+1}$ obeys the relation $U(a,\Lambda)\phi(x)U(a,\Lambda)^{-1}=\phi(\Lambda x+a)$ where $(a,\Lambda)$ is an element of the Poincar\'e group $\Pg$ and $U:(a,\Lambda)\to U(a,\Lambda)$ is its unitary representation on quantum vector states. It expresses the fact that Poincar\'e transformations are being unitary implemented. It has a classical analogy where field covariance shows that Poincar\'e transformations are canonically implemented. Covariance is self-reproducing: products of covariant fields are covariant. We recall these properties and use them to formulate the notion of covariant quantum fields on noncommutative spacetimes. In this way all our earlier results on dressing, statistics, etc. for Moyal spacetimes are derived transparently. For the Voros algebra, covariance and the *-operation are in conflict so that there are no covariant Voros fields compatible with *, a result we found earlier. The notion of Drinfel'd twist underlying much of the preceding discussion is extended to discrete abelian and nonabelian groups such as the mapping class groups of topological geons. For twists involving nonabelian groups the emergent spacetimes are nonassociative.

Signature-change events in emergent spacetimes with anisotropic scaling

We investigate the behaviour of quantum fields coupled to a spacetime geometry exhibiting finite regions of Euclidean (Riemannian) signature. Although from a gravity perspective this situation might seem somewhat far fetched, we will demonstrate its direct physical relevance for an explicitly realizable condensed matter system whose linearized perturbations experience an effective emergent spacetime geometry with externally controllable signature. This effective geometry is intrinsically quantum in origin, and its signature is determined by the details of the microscopic structure. At the level of the effective field theory arising from our condensed matter system we encounter explicit anisotropic scaling in time and space. Here Lorentz symmetry is an emergent symmetry in the infrared. This anisotropic scaling of time and space cures some of the technical problems that arise when working within a canonical quantisation scheme obeying strict Lorentz invariance at all scales, and so is helpful in permitting signature change events to take place.

Cosmological particle production in emergent rainbow spacetimes

We investigate cosmological particle production in spacetimes where Lorentz invariance emerges in the infrared limit, but is explicitly broken in the ultraviolet regime. Thus these models are similar to many (but not all) models of quantum gravity, where a breakdown of Lorentz invariance is expected for ultraviolet physics around the Planck/string scale. Our specific model focuses on the boost subgroup that supports CPT invariance and results in a momentum-dependent dispersion relation. Motivated by previous studies on spacetimes emerging from a microscopic substrate, we show how these modifications naturally lead to momentum-dependent rainbow metrics. Firstly, we investigate the possibility of reproducing cosmological particle production in spacetimes emerging from real Bose gases. Several papers have been written on the analogy between the kinematics of linearized perturbations in Bose–Einstein condensates and effective curved-spacetime quantum field theory. Recently we have studied the influence of nonperturbative ultraviolet corrections in time-dependent analog spacetimes, leading to momentum-dependent emergent rainbow spacetimes. We show that models involving a time-dependent microscopic interaction are suitable for mimicking quantum effects in FRW spacetimes. Within certain limits the analogy is sufficiently good to simulate relativistic quantum field theory in time-dependent classical backgrounds, and the quantum effects are approximately robust against the model-dependent modifications. Secondly, we analyze how significantly the particle production process deviates from the common picture. While very low-energy modes do not see the difference at all, some modes ‘re-enter the Hubble horizon’ during the inflationary epoch, and extreme ultraviolet modes are completely insensitive to the expansion. The analysis outlined here, because it is nonperturbative in the rainbow metric, exhibits features that cannot be extracted simply from the standard perturbative modification of particle dispersion relations. However, we also show how the final result, after many e-foldings, will approach a time-independent exponentially decaying particle spectrum.

Dual field theories in(d−1)+1emergent spacetimes from a unifying field theory ind+2spacetime

According to two-time physics, there is more to space and time than can be garnered with the ordinary formulation of physics. Two-time physics has shown that the standard model of particles and forces is successfully reproduced by a two-time field theory in four space and two time dimensions projected as a holographic image on an emergent space-time in $3+1$ dimensions. Among the successes of this approach is the resolution of the strong $CP$ problem of QCD as an outcome of the restrictions imposed by the higher symmetry structures in $4+2$ dimensions. In this paper we launch a program to construct the duals of the standard model as other holographic images of the same $4+2$ dimensional theory on a variety of emergent spacetimes in $3+1$ dimensions. These dual field theories are obtained as a family of gauge choices in the master $4+2$ field theory. In the present paper we deal with some of the simpler gauge choices which lead to interacting Klein-Gordon field theories for the conformal scalar with a predicted $\mathrm{SO}(d,2)$ symmetry in a variety of interesting curved spacetimes in $(d\ensuremath{-}1)+1$ dimensions. More challenging and more interesting gauge choices (including some that relate to mass) which are left to future work are also outlined. Through this approach we discover a new realm of previously unexplored dualities and hidden symmetries that exist both in the macroscopic and microscopic worlds, at the classical and quantum levels. Such phenomena predicted by Two time physics (2T-physics) can in principle be confirmed both by theory and experiment. One time physics (1T-physics) can be used to analyze the predictions but in most instances gives no clue that the predicted phenomena exist in the first place. This point of view suggests a new paradigm for the construction of a fundamental theory that is likely to impact on the quest for unification.

Planck-scale modified dispersion relations and Finsler geometry

A common feature of all quantum gravity (QG) phenomenology approaches is to consider a modification of the mass-shell condition of the relativistic particle to take into account quantum gravitational effects. The framework for such approaches is therefore usually set up in the cotangent bundle (phase space). However it was recently proposed that this phenomenology could be associated with an energy dependent geometry that has been coined ``rainbow metric''. We show here that the latter actually corresponds to a Finsler geometry, the natural generalization of Riemannian geometry. We provide in this way a new and rigorous framework to study the geometrical structure possibly arising in the semiclassical regime of QG. We further investigate the symmetries in this new context and discuss their role in alternative scenarios like Lorentz violation in emergent spacetimes or deformed special relativity-like models.