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A. Tureanu

Publications and source records attributed to A. Tureanu.

At least 19 recordsLinked to original sources
arXiv2021

Amorphous solids as fuzzy crystals: A Debye-like theory of low-temperature specific heat

We construct a quantum mechanical model of perfectly isotropic amorphous solids as fuzzy crystals and establish an analytical theory of vibrations for glasses at low temperature. Our theoretical framework relies on the basic principle that the disorder in a glass is similar to the disorder in a classical fluid, while the latter is mathematically encoded by noncommutative coordinates in the Lagrange formulation of fluid mechanics. We find that the density of states in the acoustic branches flattens significantly, leading naturally to a boson peak in the specific heat as a manifestation of a van Hove singularity. The model is valid in the same range as Debye's theory, namely up to circa 10% of the Debye temperature. Within this range, we find an excellent agreement between the theoretical predictions and the experimental data for two typical glasses, a-GeO$_2$ and Ba$_{8}$Ga$_{16}$Sn$_{30}$-clathrate. Our model supports the conceptual understanding of the nature of the boson peak in glasses as a manifestation of the liquid-like disorder. At the same time, it provides a novel, mathematically simple framework for a unitary treatment of thermodynamical and transport properties of amorphous materials and a solid background for inserting further elements of complexity specific to particular glasses.

cond-mat.dis-nn↗
arXiv2018

Quantum structure of glasses and the boson peak: a theory of vibrations

We present a novel analytical model for glasses, starting from the first principle that the disorder in a glass mimics the disorder in a fluid. The origin of the boson peak is attributed to the intrinsically noncommutative geometry of the fluid disorder, which induces a van Hove singularity in the vibrational density of states. The universality of the model is exhibited by applying it to amorphous silicon, vitreous GeO$_2$ and Ba$_{8}$Ga$_{16}$Sn$_{30}$ clathrate, which show a remarkable agreement between the theoretical predictions for specific heat and the experimental data.

cond-mat.dis-nn↗
arXiv2015

How unimodular gravity theories differ from general relativity at quantum level

We investigate path integral quantization of two versions of unimodular gravity. First a fully diffeomorphism-invariant theory is analyzed, which does not include a unimodular condition on the metric, while still being equivalent to other unimodular gravity theories at the classical level. The path integral has the same form as in general relativity (GR), except that the cosmological constant is an unspecified value of a variable, and it thus is unrelated to any coupling constant. When the state of the universe is a superposition of vacuum states, the path integral is extended to include an integral over the cosmological constant. Second, we analyze the standard unimodular theory of gravity, where the metric determinant is fixed by a constraint. Its path integral differs from the one of GR in two ways: the metric of spacetime satisfies the unimodular condition only in average over space, and both the Hamiltonian constraint and the associated gauge condition have zero average over space. Finally, the canonical relation between the given unimodular theories of gravity is established.

hep-th↗
arXiv2015

Analogy between the Schwarzschild solution in a noncommutative gauge theory and the Reissner-Nordström metric

We study modifications of the Schwarzschild solution within the noncommutative gauge theory of gravity. In the present analysis, the deformed solutions are obtained by solving the field equations perturbatively, up to the second order in the noncommutativity parameter $Θ$, for both exterior and interior solutions of the equations of motion for $e_μ^a \left(x\right)$. Remarkably, we find that this new noncommutive solution is analogous to the Reissner-Nordström solution in the ordinary spacetime, in which the square of electric charge is replaced by the square of the noncommutativity parameter, but with opposite sign. This amounts to the noncommutative Schwarzschild radius $r_{NCS}$ becoming larger than the usual radius $r_S =2M$, instead of smaller as it happens to the Reissner-Nordström radius $r_{RN}$, implying that $r_{NCS}>r_{S} >r_{RN}$. An intuitive interpretation of this result is mentioned.

hep-th↗
arXiv2014

Standard Model and Graviweak Unification with (Super)Renormalizable Gravity. Part I: Visible and Invisible Sectors of the Universe

We develop a self-consistent $Spin(4,4)$-invariant model of the unification of gravity with weak $SU(2)$ gauge and Higgs fields in the visible and invisible sectors of our Universe. We consider a general case of the graviweak unification, including the higher-derivative super-renormalizable theory of gravity, which is a unitary, asymptotically-free and perturbatively consistent theory of the quantum gravity.

hep-ph↗
arXiv2013

Gravi-Weak Unification and Multiple Point Principle

We construct a model unifying gravity with weak $SU(2)$ gauge and "Higgs" scalar fields. We assume the existence of a visible and an invisible (hidden) sector of the Universe. We used the extension of Plebanski's 4-dimensional gravitational theory, in which the fundamental fields are two-forms containing tetrads, spin connections and additional auxiliary fields. Considering a $Spin(4,4)$ invariant extended Plebanski action, we recover the actions in both (visible and invisible) sectors of the Universe. After symmetry breaking of the graviweak (GW) unification, its physical constants (Newton's constants, cosmological constants, YM-couplings, etc.), are determined by a parameter $g_{uni}$ of the GW unification. It is discussed that if this "Higgs" field coming in the GW unification could be the Higgs of the Standard Model, then the idea that its vacuum value could be, according to the Multiple Point Principle, a second minimum of the Higgs field effective potential, turns out not to be viable. Then other scalar "Higgs" field, giving the inflation and axion fields, has a Planck scale expectation value, and could have a better chance of being the scalar field unified with gravity.

hep-ph↗
arXiv2013

Quantum Black Holes, Elliptic Genera and Spectral Partition Functions

We study M-theory and D-brane quantum partition functions for microscopic black hole ensembles within the context of the AdS/CFT correspondence in terms of highest weight representations of infinite-dimensional Lie algebras, elliptic genera, and Hilbert schemes, and describe their relations to elliptic modular forms. The common feature in our examples lie in the modular properties of the characters of certain representations of the pertinent affine Lie algebras, and in the role of spectral functions of hyperbolic three-geometry associated with q-series in the calculation of elliptic genera. We present new calculations of supergravity elliptic genera on local Calabi-Yau threefolds in terms of BPS invariants and spectral functions, and also of equivariant D-brane elliptic genera on generic toric singularities. We use these examples to conjecture a link between the black hole partition functions and elliptic cohomology.

hep-th↗
arXiv2013

Graviweak Unification, Invisible Universe and Dark Energy

We consider a Graviweak Unification model with the assumption of the existence of the hidden (invisible) sector of our Universe parallel to the visible world. This Hidden World (HW) is assumed to be a Mirror World (MW) with broken mirror parity. We start with a diffeomorphism invariant theory of a gauge field valued in a Lie algebra g, which is broken spontaneously to the direct sum of the spacetime Lorentz algebra and the Yang-Mills algebra: $\tilde {\mathfrak g} = {\mathfrak su}(2)^{(grav)}_L \oplus {\mathfrak su}(2)_L$ -- in the ordinary world, and $\tilde {\mathfrak g}' = {{\mathfrak su}(2)'}^{(grav)}_R \oplus {\mathfrak su}(2)'_R$ -- in the hidden world. Using an extension of the Plebanski action for general relativity, we recover the actions for gravity, SU(2) Yang-Mills and Higgs fields in both (visible and invisible) sectors of the Universe, and also the total action. After symmetry breaking, all physical constants, including the Newton's constants, cosmological constants, Yang-Mills couplings, and other parameters, are determined by a single parameter $g$ presented in the initial action, and by the Higgs VEVs. The Dark Energy problem of this model predicts a too large supersymmetric breaking scale ($\sim 10^{10}-10^{12}$ GeV), which is not within the reach of the LHC experiments.

hep-th↗
arXiv2013

BRST-Invariant Deformations of Geometric Structures in Topological Field Theories

We study a Lie algebra of formal vector fields $W_n$ with its application to the perturbative deformed holomorphic symplectic structure in the A-model, and a Calabi-Yau manifold with boundaries in the B-model. A relevant concept in the vertex operator algebra and the BRST cohomology is that of the elliptic genera (the one-loop string partition function). We show that the elliptic genera can be written in terms of spectral functions of the hyperbolic three-geometry (which inherits the cohomology structure of BRST-like operator). We show that equivalence classes of deformations are described by a Hochschild cohomology theory of the DG-algebra ${\mathfrak A} = (A, Q)$, $Q =\bar{\partial}+\partial_{\rm deform}$, which is defined to be the cohomology of $(-1)^n Q +d_{\rm Hoch}$. Here $\bar{\partial}$ is the initial non-deformed BRST operator while $\partial_{\rm deform}$ is the deformed part whose algebra is a Lie algebra of linear vector fields ${\rm gl}_n$. We discuss the identification of the harmonic structure $(HT^\bullet(X); HΩ_\bullet(X))$ of affine space $X$ and the group ${\rm Ext}_{X}^n({\cal O}_{\triangle}, {\cal O}_{\triangle})$ (the HKR isomorphism), and bulk-boundary deformation pairing.

math-ph↗
arXiv2013

Quantum Corrections to Bekenstein-Hawking Black Hole Entropy and Gravity Partition Functions

Algebraic aspects of the computation of partition functions for quantum gravity and black holes in $AdS_3$ are discussed. We compute the sub-leading quantum corrections to the Bekenstein-Hawking entropy. It is shown that the quantum corrections to the classical result can be included systematically by making use of the comparison with conformal field theory partition functions, via the $AdS_3/CFT_2$ correspondence. This leads to a better understanding of the role of modular and spectral functions, from the point of view of the representation theory of infinite-dimensional Lie algebras. Besides, the sum of known quantum contributions to the partition function can be presented in a closed form, involving the Patterson-Selberg spectral function. These contributions can be reproduced in a holomorphically factorized theory whose partition functions are associated with the formal characters of the Virasoro modules. We propose a spectral function formulation for quantum corrections to the elliptic genus from supergravity states.

hep-th↗
arXiv2012

Gravity and Mirror Gravity in Plebanski Formulation

We present several theories of four-dimensional gravity in the Plebanski formulation, in which the tetrads and the connections are the independent dynamical variables. We consider the relation between different versions of gravitational theories: Einstenian, dual, 'mirror' gravities and gravity with torsion. According to Plebanski's assumption, our world, in which we live, is described by the self-dual left-handed gravity. We propose that if the Mirror World exists in Nature, then the 'mirror gravity' is the right-handed anti-self-dual gravity with broken mirror parity. Considering a special version of the Riemann--Cartan space-time, which has torsion as additional geometric property, we have shown that in the Plebanski formulation the ordinary and dual sectors of gravity, as well as the gravity with torsion, are equivalent. In this context, we have also developed a 'pure connection gravity' -- a diffeomorphism-invariant gauge theory of gravity. We have calculated the partition function and the effective Lagrangian of this four-dimensional gravity and have investigated the limit of this theory at small distances.

gr-qc↗
arXiv2012

Thermal Casimir-Polder interaction of different atoms with graphene

The thermal correction to the energy of Casimir-Polder interaction of atoms with a suspended graphene membrane described by the Dirac model is investigated. We show that a major impact on the thermal correction is made by the size of the gap in the energy spectrum of graphene quasiparticles. Specifically, if the temperature is much smaller than the gap parameter (alternatively, larger or of the order of the gap parameter), the thermal correction is shown to be relatively small (alternatively, large). We have calculated the free energy of the thermal Casimir-Polder interaction of atoms of He, Na, Rb, and Cs with graphene described by both the hydrodynamic and Dirac models. It is shown that in exact computations using the Dirac model, one should use the polarization operator at nonzero temperature. The computational results for the Casimir-Polder free energy obtained in the framework of hydrodynamic model of graphene are several times larger than in the Dirac model within the separation region below 2$μ$m. We conclude that the theoretical predictions following from the two models can be reliably discriminated in experiments on quantum reflection of different atoms on graphene.

quant-ph↗
arXiv2012

Extended Poincaré supersymmetry in three dimensions and supersymmetric anyons

We classify the unitary representations of the extended Poincaré supergroups in three dimensions. Irreducible unitary representations of any spin can appear, which correspond to supersymmetric anyons. Our results also show that all irreducible unitary representations necessarily have physical momenta. This is in sharp contrast to the ordinary Poincaré group in three dimensions, that admits in addition irreducible unitary representations with non-physical momenta, which are discarded on physical grounds.

hep-th↗
arXiv2011

Mirror World and Superstring-Inspired Hidden Sector of the Universe, Dark Matter and Dark Energy

We develop a concept of parallel existence of the ordinary (O) and hidden (H) worlds. We compare two cases: 1) when the hidden sector of the Universe is a mirror counterpart of the ordinary world, and 2) when it is a superstring-inspired shadow world described, in contrast to the mirror world, by a symmetry group (or by a chain of groups), which does not coincide with the ordinary world symmetry group. We construct a cosmological model assuming the existence of the superstring-inspired E_6 unification, broken at the early stage of the Universe to SO(10)\times U(1)_Z - in the O-world, and to SU(6)'\times SU(2)'_θ- in the H-world. As a result, we obtain the low energy symmetry group G'_SM\times SU(2)'_θin the shadow world, instead of the Standard Model group G_SM existing in the O-world. The additional non-Abelian SU(2)'_θgroup with massless gauge fields, "thetons", is responsible for dark energy. Considering a quintessence model of cosmology with an inflaton σand an axion a_θ, which is a pseudo Nambu-Goldstone boson induced by the SU(2)'_θ-group anomaly, we explain the origin of Dark Energy, Dark Matter and Ordinary Matter. In the present model we review all cosmological epochs (inflation, reheating, recombination and nucleosynthesis), and give our version of the baryogenesis. The cosmological constant problem is also briefly discussed.

hep-ph↗
arXiv2011

E6 Unification and the Hidden Sector of the Universe

A talk presents a new cosmological model with superstring-inspired $E_6$ unification, broken at the early stage of the Universe into $SO(10)\times U(1)_Z$ -- into the ordinary world, and $SU(6)'\times SU(2)'_θ$ -- into the hidden world.

hep-ph↗
arXiv2011

Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory

We propose new Wightman functions as vacuum expectation values of products of field operators in the noncommutative space-time. These Wightman functions involve the $\star$-product among the fields, compatible with the twisted Poincaré symmetry of the noncommutative quantum field theory (NC QFT). In the case of only space-space noncommutativity ($θ_{0i}=0$), we prove the CPT theorem using the noncommutative form of the Wightman functions. We also show that the spin-statistics theorem, demonstrated for the simplest case of a scalar field, holds in NC QFT within this formalism.

hep-th↗
arXiv2010

Baryogenesis in Cosmological Model with Superstring-Inspired E_6 Unification

We have developed a concept of parallel existence of the ordinary (O) and hidden (H) worlds with a superstring-inspired E_6 unification, broken at the early stage of the Universe into SO(10) X U(1) - in the O-world, and SU(6)' X SU(2)' - in the H-world. As a result, we have obtained in the hidden world the low energy symmetry group G'_SM X SU(2)'_θ, instead of the Standard Model group G_SM. The additional non-Abelian SU(2)'_θgroup with massless gauge fields, "thetons", is responsible for the dark energy. We present a baryogenesis mechanism with the B-L asymmetry produced by the conversion of ordinary leptons into particles of the hidden sector.

hep-ph↗