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Register a new userHolography on tessellations of hyperbolic space
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We compute boundary correlation functions for scalar fields on tessellations of two- and three-dimensional hyperbolic geometries. We present evidence that the continuum relation between the scalar bulk mass and the scaling dimension associated with boundary-to-boundary correlation functions survives the truncation of approximating the continuum hyperbolic space with a lattice.
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Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis.
We discuss the possible validity in QCD of a relation between Greens functions which has been recently suggested by Son and Yamamoto, based on a class of AdS/CFT-inspired models of QCD. Our conclusion is that the relation in question is unlikely to be implemented in QCD.
We consider deep inelastic scattering (DIS) on a nucleus described using a density expansion. In leading order, the scattering is dominated by the incoherent scattering on individual nucleons distributed using the Thomas-Fermi approximation. We use the holographic structure functions for DIS scattering on single nucleons to make a non-perturbative estimate of the nuclear structure function in leading order in the density. Our results are compared to the data in the large-x regime.
The Light Front Holographic (LFH) wave equation, which is the conformal scalar equation on the plane, is revisited from the perspective of the supersymmetric quantum mechanics, and attention is drawn to the fact that it naturally emerges in the small hyperbolic angle approximation to the curved Higgs oscillator on the hyperbolic plane, i.e. on the upper part of the two-dimensional hyperboloid of two sheets, a space of constant negative curvature. Such occurs because the particle dynamics under consideration reduces to the one dimensional Schrodinger equation with the second hyperbolic Poschl-Teller potential, whose flat-space (small-angle) limit reduces to the conformally invariant inverse square distance plus harmonic oscillator interaction, on which LFH is based. In consequence, energies and wave functions of the LFH spectrum can be approached by the solutions of the Higgs oscillator on the hyperbolic plane in employing its curvature and the potential strength as fitting parameters. Also the proton electric charge form factor is well reproduced within this scheme by means of a Fourier-Helgason hyperbolic wave transform of the charge density. In conclusion, in the small angle approximation, the Higgs oscillator on the hyperbolic plane is demonstrated to satisfactory parallel essential outcomes of the Light Front Holographic QCD. The findings are suggestive of associating the hyperboloid curvature of the with a second scale in LFH, which then could be employed in the definition of a chemical potential.
The type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. In the Lorentzian version, in particular, the emergence of (3+1)D expanding space-time was observed by Monte Carlo studies of this model. Here we provide new perspectives on the (3+1)D expanding space-time that have arised from recent studies. First it was found that the matrix configurations generated by the simulation are singular in that the submatrices representing the expanding 3D space have only two large eigenvalues associated with the Pauli matrices. This problem was conjectured to occur due to the approximation used to avoid the sign problem in simulating the model. In order to confirm this conjecture, the complex Langevin method was applied to overcome the sign problem instead of using the approximation. The results indeed showed a clear departure from the Pauli-matrix structure, while the (3+1)D expanding behavior remained unaltered. It was also found that classical solutions obtained within a certain ansatz show quite generically a (3+1)D expanding behavior with smooth space-time structure.
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