Pavle Midodashvili
We analyze the limits that quantum mechanics imposes on the accuracy to which $(4+n)$-dimensional spacetime geometry can be measured. Using physics of computation and light sheet concept we derive explicit expressions for quantum fluctuations and explore their cumulative effects for various spacetime foam models.
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We study renormalization group flows in unitary two dimensional sigma models with asymptotically flat target spaces. Applying an infrared cutoff to the target space, we use the Zamolodchikov c-theorem to demonstrate that the target space ADM energy of the UV fixed point is greater than that of the IR fixed point: spacetime energy decreases under world-sheet RG flow. This result mirrors the well understood decrease of spacetime Bondi energy in the time evolution process of tachyon condensation.
The complete set of solutions of two dimensional classical string theory are constructed for any curved spacetime. They describe folded strings moving in curved spacetime. Surprizing stringy behavior becomes evident at singularities such as black holes.The solutions are given in the form ofa map from the world sheet to target spacetime, where the world sheet has to be divided into lattice -like patches corresponding to different maps. A recursion relation analogous to a transfer matrix connects these maps into a single continuous map. This ``transfer matrix'' encodes the properties of the worl…
In recent papers, a model of a two-sheeted spacetime M4XZ2 was introduced and the quantum dynamics of massive fermions was studied in this framework. In the present study, we show that the physical predictions of the model are perfectly consistent with observations and most important, it can solve the puzzling problem of the four-dimensional localization of the fermion species in multidimensional spacetimes. It is demonstrated that fermion localization on the sheets arises from the combination of the discrete bulk structure and environmental interactions. The mechanism described in this paper …
The symmetries of two-dimensional supersymmetric sigma models on target spaces with covariantly constant forms associated to special holonomy groups are analysed. It is shown that each pair of such forms gives rise to a new one, called a Nijenhuis form, and that there may be further reductions of the structure group. In many cases of interest there are also covariantly constant one-forms which also give rise to symmetries. These geometries are of interest in the context of heterotic supergravity solutions and the associated reductions are studied from a spacetime point of view via the Killing …
The Two-Sheeted Topology of Extended Kerr-Type Spacetimes and a Parity-of-Crossings Property for Ring-Traversing Geodesics
本文研究了扩展的 Kerr 型时空的双叶拓扑结构，并证明了穿过环奇点的测地线具有奇偶性性质。
In this paper, we explore the implications of a two-point discretization of an extra-dimension in a five-dimensional quantum setup. We adopt a pragmatic attitude by considering the dynamics of spin-half particles through the simplest possible extension of the existing Dirac and Pauli equations. It is shown that the benefit of this approach is to predict new physical phenomena while maintaining the number of constitutive hypothesis at minimum. As the most striking feature of the model, we demonstrate the possibility of fermionic matter oscillations between the two four-dimensional sections and …
World-sheet and spacetime supersymmetries that are manifest in some string backgrounds may not be so in their T-duals. Nevertheless, they always remain symmetries of the underlying conformal field theory. In previous work the mechanism by which T-duality destroys manifest supersymmetry and gives rise to non-local realizations was found. We give the general conditions for a 2-dim N=1 supersymmetric sigma-model to have non-local and hence non-manifest extended supersymmetry. We then examine T-duality as a mechanism of restoring manifest supersymmetry. This happens whenever appropriate combinatio…
Our universe seems to be radiation dominated at early times, and vacuum energy dominated at late times. When we consider the maximal analytic extension of this spacetime, its symmetries and complex analytic properties suggest a picture in which spacetime has two sheets, exchanged by an isometry which, in turn, picks a preferred (CPT-symmetric) vacuum state for quantum fields on the spacetime. Previously (arXiv:1803.08928, arXiv:1803.08930), we showed how this line of thought provides new explanations for dark matter, the matter-antimatter asymmetry, the absence of primordial vector and tensor …
We investigate the quantization of the bosonic string model which has a local U(1)_V * U(1)_A gauge invariance as well as the general coordinate and Weyl invariance on the world-sheet. The model is quantized by Lagrangian and Hamiltonian BRST formulations {á} la Batalin, Fradkin and Vilkovisky and noncovariant light-cone gauge formulation. Upon the quantization the model turns out to be formulated consistently in 26+2-dimensional background spacetime involving two time-like coordinates.
A possible generalisation is given to the meaning of maximal symmetry in the presence of torsion
We construct a Neveu-Schwarz-Ramond superstring model which is invariant under supersymmetric U(1)_V * U(1)_A gauge transformations as well as the super-general coordinate, the super local Lorentz and the super-Weyl transformations on the string world-sheet. We quantize the superstring model by covariant BRST formulation a la Batalin and Vilkovisky and noncovariant light-cone gauge formulation. Upon the quantizations the model turns out to be formulated consistently in 10+2-dimensional background spacetime involving two time dimensions.
We show that in AB stacked bilayer graphene low energy excitations around the semimetallic points are described by massless, four dimensional Dirac fermions. There is an effective reconstruction of the 4 dimensional spacetime, including in particular the dimension perpendicular to the sheet, that arises dynamically from the physical graphene sheet and the interactions experienced by the carriers. The effective spacetime is the Eisenhart-Duval lift of the dynamics experienced by Galilei invariant Lévy-Leblond spin $\frac{1}{2}$ particles near the Dirac points. We find that changing the intrinsi…
An arithmetic framework to string compactification is described. The approach is exemplified by formulating a strategy that allows to construct geometric compactifications from exactly solvable theories at $c=3$. It is shown that the conformal field theoretic characters can be derived from the geometry of spacetime, and that the geometry is uniquely determined by the two-dimensional field theory on the world sheet. The modular forms that appear in these constructions admit complex multiplication, and allow an interpretation as generalized McKay-Thompson series associated to the Mathieu and Con…
We outline how QED with spinor matter can be described by the tensionless limit of spinning strings with contact interactions. The strings represent electric lines of force with charges at their ends. The contact interaction is constructed from a delta-function on the world-sheet which, although off-shell, decouples from the world-sheet metric. Integrating out the string degrees of freedom with fixed boundary generates the super-Wilson loop that couples spinor matter to electromagnetism in the world-line formalism. World-sheet and world-line, but not spacetime, supersymmetry underpin the model…
We analyze in detail the possible breaking of spacetime supersymmetry under T-duality transformations. We find that when appropiate world-sheet effects are taken into account apparent puzzles concerning supersymmetry in spacetime are solved. We study T-duality in general heterotic $σ$-models analyzing possible anomalies, and we find some modifications of Buscher's rules. We then work out a simple but representative example which contains most of the difficulties. We also consider the issue of supersymmetry versus duality for marginal deformations of WZW models and present a mechanism that rest…
This is the first of a series of papers in which we use analyticity properties of quantum fields propagating on a spacetime to uncover a new multiverse geometry when the classical geometry has horizons and/or singularities. The nature and origin of the multiverse idea presented in this paper, that is shared by the fields in the standard model coupled to gravity, is different from other notions of a multiverse. Via analyticity we are able to establish definite relations among the universes. In this paper we illustrate these properties for the extended Rindler space, while black hole spacetime a…
We use the conservation law of the stress-energy and spin tensors to study the motion of massive brane-like objects in Riemann-Cartan geometry. The world-sheet equations and boundary conditions are obtained in a manifestly covariant form. In the particle case, the resultant world-line equations turn out to exhibit a novel spin-curvature coupling. In particular, the spin of a zero-size particle does not couple to the background curvature. In the string case, the world-sheet dynamics is studied for some special choices of spin and torsion. As a result, the known coupling to the Kalb-Ramond antis…
The unitarity problem in curved spacetime is solved for the string described by the SL(2,R) WZW model. The spectrum is computed exactly and demonstratedto be ghost-free. The new features include (i) SL(2,R) left/right symmetrycurrents that have logarithmic cuts on the world sheet but that satisfy theusual local operator products or commutation rules, (ii) physical statesconsistent with the monodromy condition of closed strings despite thelogarithmic singularity in the currents, and (iii) a new free boson realization for these currents which render the SL(2,R) WZW model completely solvable.
We study quantum strings in strong gravitational fields. The relevant small parameter is $g=R_c{\sqrt T_0}$, where $R_c$ is the curvature of the spacetime and $T_0$ is the string tension. Within our systematic expansion we obtain to zeroth order the null string (string with zero tension), while the first order correction incorporates the string dynamics. We apply our formalism to quantum null strings in de Sitter spacetime. After a reparametrization of the world-sheet coordinates, the equations of motion are simplified. The quantum algebra generated by the constraints is considered, ordering t…
To understand in detail the contribution of a world-sheet instanton to the superpotential in a heterotic string compactification, one has to understand the moduli dependence (bundle and complex structure moduli) of the one-loop determinants from the fluctuations, which accompany the classical exponential contribution (involving Kähler moduli) when evaluating the world-volume partition function. Here we use techniques to describe geometrically these Pfaffians for spectral bundles over rational base curves in elliptically fibered Calabi-Yau threefolds, and provide a (partially exhaustive) list o…
If we assume that there is the ultimate thoery at all, how should the concept of the spacetime be formulated? The following essay is my consideration on such a question. The use of mathematical expressions is suppressed as long as possible. Any criticism on my opinion is welcome.
In a recent paper, a model for describing the quantum dynamics of massive particles in a non-commutative two-sheeted spacetime was proposed. This model considers a universe made with two spacetime sheets embedded in a 5D bulk where the fifth dimension is restricted to only two points. It was shown that this construction has several important consequences for the quantum dynamics of massive particles. Most notably, it was demonstrated that a coupling arises between the two sheets allowing matter exchange in presence of intense magnetic vector potentials. In this paper, we show that non-commutat…
After many years, the deep nature of spacetime in string theory remains an enigma. In this letter we incorporate the concept of Born reciprocity in order to provide a new point of view on string theory in which spacetime is a derived dynamical concept. This viewpoint may be thought of as a dynamical chiral phase space formulation of string theory, in which Born reciprocity is implemented as a choice of a Lagrangian submanifold of the phase space, and amounts to a generalization of T-duality. In this approach the fundamental symmetry of string theory contains phase space diffeomorphism invarian…
We demonstrate that an impulse action (`recoil') on a D-particle embedded in a (four-dimensional) cosmological Robertson-Walker (RW) spacetime is described, in a $σ$-model framework, by a suitably extended higher-order logarithmic world-sheet algebra of relevant deformations. We study in some detail the algebra of the appropriate two-point correlators, and give a careful discussion as to how one can approach the world-sheet renormalization group infrared fixed point, in the neighborhood of which the logarithmic algebra is valid. It is found that, if the initial RW spacetime does not have cosmo…
Exact and explicit string solutions in de Sitter spacetime are found. (Here, the string equations reduce to a sinh-Gordon model). A new feature without flat spacetime analogy appears: starting with a single world-sheet, several (here two) strings emerge. One string is stable and the other (unstable) grows as the universe grows. Their invariant size and energy either grow as the expansion factor or tend to constant. Moreover, strings can expand (contract) for large (small) universe radius with a different rate than the universe.
The causal set approach to quantum gravity embodies the concepts of causality and discreteness. This article explores some foundational and conceptual issues within causal set theory.
Stochastic Description of Near-Horizon Fluctuations in Rindler-AdS
本文在 AdS/CFT 框架下用 Planck 宽度抹平的随机量子源将近视界 Einstein 方程化为 Langevin 方程，证明光面涨落会导致光子往返时间产生依赖 $G_N^{(d)}$ 与 $L$ 的累积效应。
Minimax surfaces and the holographic entropy cone
本文证明HRT熵的minimax曲面表述以时空同调刻画纠缠楔，并据此探讨时变态的加权图模型及RT与HRT熵锥重合的条件。
The representation of measurements by positive operator valued measures and the description of the most general state transformations by means of completely positive maps are two basic concepts of quantum information theory. These concepts can be trivially extended to field theories in curved spacetime if all the representations of canonical commutation or anticommutation relations are unitarily equivalent. We show that both concepts can be applied even when there is no such unitary equivalence.
Quantum Spacetime: Echoes of basho
本文探讨basho概念如何为理解量子引力中点的概念提供新视角，强调量子时空对几何学的重新思考。
In case of spacetimes with single horizon, there exist several well-established procedures for relating the surface gravity of the horizon to a thermodynamic temperature. Such procedures, however, cannot be extended in a straightforward manner when a spacetime has multiple horizons. In particular, it is not clear whether there exists a notion of global temperature characterizing the multi-horizon spacetimes. We examine the conditions under which a global temperature can exist for a spacetime with two horizons using the example of Schwarzschild-De Sitter (SDS) spacetime. We systematically exten…
Geometrical analysis of a new type of Unified Field Theoretical models follow the guidelines of previous works of the authors is presented. These new unified theoretical models are characterized by an underlying hypercomplex structure, zero non-metricity and the geometrical action is determined fundamentally by the curvature provenient of the breaking of symmetry of a group manifold in higher dimensions. This mechanism of Cartan-MacDowell-Mansouri type, permits us to construct geometrical actions of determinantal type leading a non topological physical Lagrangian due the splitting of a reducti…
A physically meaningful local concept of temperature is introduced in quantum field theory on curved spacetime and applied to the example of a massless field on de Sitter space. It turns out in this model that the equilibrium (Gibbs) states which can be prepared by a geodesic observer have in general a varying temperature distribution in the neighborhood of the geodesic and may not even allow for a consistent thermal interpretation close to the horizon. This result, which can be traced back to the Unruh effect, illustrates the failure of a global notion of temperature in curved spacetime and r…
Over the last years the Asymptotic Safety program has matured into a serious candidate for a quantum theory of gravity compatible with observations. The rapid technical progress in computing renormalisation group flows for gravity and gravity-matter systems in the non-perturbative regime has put many interesting physical questions within reach. In particular, the construction of the non-perturbative quantum corrections to the propagation of fields on a fluctuating spacetime allows addressing the effective propagation of matter on a quantum spacetime or the possible resolution of spacetime sing…
There has been recent interest in identifying entanglement as the fundamental concept from which space may emerge. We note that the particular way that a Hilbert space is decomposed into tensor factors is important in what the resulting geometry looks like. We then propose that time may be regarded as a variable that parameterizes a family of such decompositions, thus giving rise to a family of spatial geometries. As a proof of concept, this idea is demonstrated in two toy models based on Kitaev's toric code, which feature a dynamical change of dimension and topology.
We consider the $\varrho$-Minkowski spacetime, a model with linear noncommutativity involving the time and the azimuthal angle. We study its quantum symmetries, the $\varrho$-Poincaré quantum group, and analyse the concepts of localizability and quantum observers.
We briefly review two recently developed extensions of the Lorentzian geometry of spacetime and prove that they are in fact closely related. The first is the concept of observer space, which generalizes the space of Lorentzian observers, i.e., future unit timelike vectors, using Cartan geometry. The second is the concept of Finsler spacetimes, which generalizes the Lorentzian metric of general relativity to an observer-dependent Finsler metric. We show that every Finsler spacetime possesses a well-defined observer space that can naturally be equipped with a Cartan geometry. Conversely, we deri…
There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 10^(69) bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light-sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. We explain how the bound is tested and demonstrate its validity in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet …
The conditional probabilities and the empirical laws in a free scalar QFT in curved spacetime
针对弯曲时空量子场论经验定律存在概念模糊性的问题，本文提出用无初始态信息的先验条件概率描述其部分经验定律，给出了自由标量场相关的经验定律示例。
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