Browsing by Author "Bianchi, Ernesto"

Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    Bulk renormalization and the AdS/CFT correspondence
    (2023) Banados, Maximo; Bianchi, Ernesto; Munoz, Ivan; Skenderis, Kostas
    We develop a systematic renormalization procedure for QFT in anti-de Sitter spacetime. UV infinities are regulated using a geodesic point-splitting method, which respects AdS isometries, while IR infinities are regulated by cutting off the radial direction (as in holographic renormalization). The renormalized theory is defined by introducing Z factors for all parameters in the Lagrangian and the boundary conditions of bulk fields (sources of dual operators), and a boundary counterterm action, Sct, such that the limit of removing the UV and IR regulators exists. The results are in general scheme dependent (mirroring the analogous result in flat space) and require renormalization conditions. These may be provided by the dual CFT (or by string theory in AdS). Our analysis amounts also to a first principles derivation of the Feynman rules regarding Witten diagrams. The presence and treatment of IR divergences is essential for correctly accounting for anomalous dimensions of dual operators. We apply the method to scalar phi 4 theory and obtain the renormalized two-point function of the dual operator to two loops, and the renormalized four-point function to one-loop order, for operators of any dimension Delta and bulk spacetime dimension up to d+1=7.
  • No Thumbnail Available
    Item
    Elastic anomalies in glasses: Elastic string theory understanding of the cases of glycerol and silica
    (2020) Bianchi, Ernesto; Giordano, Valentina M.; Lund, Fernando
    In this work we present an implementation of the analytical string theory recently applied to the description of glasses. These are modeled as continuum media with embedded elastic string heterogeneities, randomly located and randomly oriented, which oscillate around a straight equilibrium position with a fundamental frequency depending on their length. The existence of a length distribution is reflected then in a distribution of oscillation frequencies which is responsible for the boson peak in the glass density of states. Previously, it has been shown that such a description can account for the elastic anomalies reported at frequencies comparable with the boson peak: the strong phonon scattering and the negative dispersion in the sound velocity, as a result of the interference of the string oscillations with propagating sound plane waves. Here we start from the generalized hydrodynamics to determine the dynamic correlation function S(k, omega) associated with the coherent, dispersive, and attenuated sound waves resulting from such interference. We show that once the vibrational density of states has been measured, we can use it for unambiguously fixing the string length distribution inherent to a given glass. The density-density correlation function obtained using such distribution is strongly constrained, and able to account for the experimental data collected on two prototypical glasses with very different microscopic structure and fragility: glycerol and silica. The obtained string length distribution is compatible with the typical size of elastic heterogeneities previously reported for silica and supercooled liquids, and the atomic motion associated with the string dynamics is consistent with the soft modes recently identified in large-scale numerical simulations as nonphonon modes responsible for the boson peak. The theory is thus in agreement with the most recent advances in the understanding of the glass-specific dynamics and offers an appealing, simple understanding of the microscopic origin of the latter, while raising new questions on the universality or material specificity of the string distribution properties.