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Tomasz R. Taylor - One of the best experts on this subject based on the ideXlab platform.
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On Sugawara construction on Celestial Sphere
Journal of High Energy Physics, 2020Co-Authors: Wei Fan, Stephan Stieberger, Angelos Fotopoulos, Tomasz R. TaylorAbstract:Conformally soft gluons are conserved currents of the Celestial Conformal Field Theory (CCFT) and generate a Kac-Moody algebra. We study Celestial amplitudes of Yang-Mills theory, which are Mellin transforms of gluon amplitudes and take the double soft limit of a pair of gluons. In this manner we construct the Sugawara energy-momentum tensor of the CCFT. We verify that conformally soft gauge bosons are Virasoro primaries of the CCFT under the Sugawara energy-momentum tensor. The Sugawara tensor though does not generate the correct conformal transformations for hard states. In Einstein-Yang- Mills (EYM) theory, we consider an alternative construction of the energy-momentum tensor, similar to the double copy construction which relates gauge theory amplitudes with gravity ones. This energy momentum tensor has the correct properties to generate conformal transformations for both soft and hard states. We extend this construction to supertranslations.
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Primary Fields in Celestial CFT
Journal of High Energy Physics, 2019Co-Authors: Angelos Fotopoulos, Tomasz R. TaylorAbstract:The basic ingredient of CCFT holography is to regard four-dimensional amplitudes describing conformal wave packets as two-dimensional conformal correlation functions of the operators associated to external particles. By construction, these operators transform as quasi-primary fields under SL(2,C) conformal symmetry group of the Celestial Sphere. We derive the OPE of the CCFT energy-momentum tensor with the operators representing gauge bosons and show that they transform as Virasoro primaries under diffeomorphisms of the Celestial Sphere.
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Strings on Celestial Sphere
Nuclear Physics B, 2018Co-Authors: Stephan Stieberger, Tomasz R. TaylorAbstract:Abstract We transform superstring scattering amplitudes into the correlation functions of primary conformal fields on two-dimensional Celestial Sphere. The points on Celestial Sphere are associated to the asymptotic directions of (light-like) momenta of external particles, with the Lorentz group realized as the S L ( 2 , C ) conformal symmetry of the Sphere. The energies are dualized through Mellin transforms into the parameters that determine dimensions of the primaries. We focus on four-point amplitudes involving gauge bosons and gravitons in type I open superstring theory and in closed heterotic superstring theory at the tree-level.
Felix Ringer - One of the best experts on this subject based on the ideXlab platform.
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Soft Fragmentation on the Celestial Sphere
Journal of High Energy Physics, 2020Co-Authors: Duff Neill, Felix RingerAbstract:We develop two approaches to the problem of soft fragmentation of hadrons in a gauge theory for high energy processes. The first approach directly adapts the standard resummation of the parton distribution function's anomalous dimension (that of twist-two local operators) in the forward scattering regime, using $k_T$-factorization and BFKL theory, to the case of the fragmentation function by exploiting the mapping between the dynamics of eikonal lines on transverse-plane to the Celestial-Sphere. Critically, to correctly resum the anomalous dimension of the fragmentation function under this mapping, one must pay careful attention to the role of regularization, despite the manifest collinear or infra-red finiteness of the BFKL equation. The anomalous dependence on energy in the Celestial case, arising due to the mismatch of dimensionality between positions and angles, drives the differences between the space-like and time-like anomalous dimension of parton densities, even in a conformal theory. The second approach adapts an angular-ordered evolution equation, but working in 4-2$\epsilon$ dimensions at all angles. The two approaches are united by demanding that the anomalous dimension in 4-2$\epsilon$ dimensions for the parton distribution function determines the kernel for the angular-ordered evolution to all orders.
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soft fragmentation on the Celestial Sphere
Journal of High Energy Physics, 2020Co-Authors: Duff Neill, Felix RingerAbstract:We develop two approaches to the problem of soft fragmentation of hadrons in a gauge theory for high energy processes. The first approach directly adapts the standard resummation of the parton distribution function’s anomalous dimension (that of twist-two local operators) in the forward scattering regime, using kT -factorization and BFKL theory, to the case of the fragmentation function by exploiting the mapping between the dynamics of eikonal lines on transverse-plane to the Celestial-Sphere. Critically, to correctly resum the anomalous dimension of the fragmentation function under this mapping, one must pay careful attention to the role of regularization, despite the manifest collinear or infra- red finiteness of the BFKL equation. The anomalous dependence on energy in the Celestial case, arising due to the mismatch of dimensionality between positions and angles, drives the differences between the space-like and time-like anomalous dimension of parton densities, even in a conformal theory. The second approach adapts an angular-ordered evolution equation, but working in 4 − 2ϵ dimensions at all angles. The two approaches are united by demanding that the anomalous dimension in 4 − 2ϵ dimensions for the parton distribution function determines the kernel for the angular-ordered evolution to all orders.
A. S. Tsvetkov - One of the best experts on this subject based on the ideXlab platform.
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Method of ignoring the systematic variations of stellar parallaxes over the Celestial Sphere in a kinematic analysis of stellar proper motions
Astronomy Letters, 2014Co-Authors: V. V. Vityazev, A. S. TsvetkovAbstract:A method for determining the velocity field parameters free from the distortions due to the systematic variations of stellar parallaxes over the Celestial Sphere is proposed. The method is based on the approximation of parallaxes as a function of coordinates on the Sphere using spherical harmonics and can be applied in those cases where the solar motion cannot be eliminated from the stellar proper motions. Numerical experiments have shown that our method is able to obtain accurate coordinates of the solar apex and to calculate the kinematic parameters of the Ogorodnikov-Milne model to within three coefficients of the decomposition of parallaxes into first-order spherical harmonics. Examples of applying the method to the stellar proper motions of the Hipparcos catalogue, which admits checking the results using trigonometric parallaxes, are provided. Such a check has been found to yield a positive result only for nearby stars at heliocentric distances that do not exceed 400 pc and for which the parallaxes were determined with a relative error of at least 30%. An interesting feature of this method is the possibility to construct the shape of the figure which is formed by the deviations of the parallaxes from the Sphere corresponding to the average parallaxes of the stars under consideration. It should be specially emphasized that all of this is done in the complete absence of information about the stellar parallaxes. The “solar terms” of the stellar proper motions that are formed by the products of the parallaxes by the solar motion components relative to the centroid of stars are the main source of information about the parallaxes here.
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Distortion of the stellar velocity field parameters due to systematic variations of parallaxes over the Celestial Sphere
Astronomy Letters, 2014Co-Authors: V. V. Vityazev, A. S. TsvetkovAbstract:We study the effect of systematic variations in stellar parallaxes over the Celestial Sphere on the results of a kinematic analysis of stellar proper motions. Our approach is based on the representation of stellar parallaxes by scalar spherical harmonics and on the decomposition of stellar proper motions into a system of vector spherical harmonics. We derive theoretical relations that relate the coefficients of the decomposition of stellar proper motions into toroidal and spheroidal harmonics to the coefficients of the decomposition of stellar parallaxes into scalar spherical harmonics. We have established that the systematic variations of parallaxes over the Celestial Sphere distort all parameters of the linear Ogorodnikov-Milne model and can be responsible for the appearance of beyond-the-model harmonics. We have performed a kinematic analysis of the proper motions of blue-white and red giants based on Hipparcos data. The parallaxes of blue-white giants show a strong dependence on Galactic latitude (with predominant contraction along the Galactic equator). In contrast, the deviations of the parallaxes from the mean for red giants are localized only in two regions of the Celestial Sphere. For these samples, the effect of parallax variations over the Celestial Sphere on kinematic parameters has turned out to be comparable to their rms errors. The global solutions performed using both samples have revealed strong beyond-the-model kinematic effects described by second-order toroidal harmonics and third-order spheroidal harmonics. Using the solutions performed separately in the northern and southern Galactic hemiSpheres, we have established that not the systematic variations of parallaxes over the Celestial Sphere but the retardation of Galactic rotation with increasing distance of stars from the principal Galactic plane is mainly responsible for the appearance of these harmonics. Based on these samples of stars, we have estimated the magnitude of the vertical Galactic rotation velocity gradient to be 18.0±2.9 and 22.7±2.2 km s−1 kpc−1, respectively.
Stephan Stieberger - One of the best experts on this subject based on the ideXlab platform.
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On Sugawara construction on Celestial Sphere
Journal of High Energy Physics, 2020Co-Authors: Wei Fan, Stephan Stieberger, Angelos Fotopoulos, Tomasz R. TaylorAbstract:Conformally soft gluons are conserved currents of the Celestial Conformal Field Theory (CCFT) and generate a Kac-Moody algebra. We study Celestial amplitudes of Yang-Mills theory, which are Mellin transforms of gluon amplitudes and take the double soft limit of a pair of gluons. In this manner we construct the Sugawara energy-momentum tensor of the CCFT. We verify that conformally soft gauge bosons are Virasoro primaries of the CCFT under the Sugawara energy-momentum tensor. The Sugawara tensor though does not generate the correct conformal transformations for hard states. In Einstein-Yang- Mills (EYM) theory, we consider an alternative construction of the energy-momentum tensor, similar to the double copy construction which relates gauge theory amplitudes with gravity ones. This energy momentum tensor has the correct properties to generate conformal transformations for both soft and hard states. We extend this construction to supertranslations.
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Strings on Celestial Sphere
Nuclear Physics B, 2018Co-Authors: Stephan Stieberger, Tomasz R. TaylorAbstract:Abstract We transform superstring scattering amplitudes into the correlation functions of primary conformal fields on two-dimensional Celestial Sphere. The points on Celestial Sphere are associated to the asymptotic directions of (light-like) momenta of external particles, with the Lorentz group realized as the S L ( 2 , C ) conformal symmetry of the Sphere. The energies are dualized through Mellin transforms into the parameters that determine dimensions of the primaries. We focus on four-point amplitudes involving gauge bosons and gravitons in type I open superstring theory and in closed heterotic superstring theory at the tree-level.
V. V. Vityazev - One of the best experts on this subject based on the ideXlab platform.
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Method of ignoring the systematic variations of stellar parallaxes over the Celestial Sphere in a kinematic analysis of stellar proper motions
Astronomy Letters, 2014Co-Authors: V. V. Vityazev, A. S. TsvetkovAbstract:A method for determining the velocity field parameters free from the distortions due to the systematic variations of stellar parallaxes over the Celestial Sphere is proposed. The method is based on the approximation of parallaxes as a function of coordinates on the Sphere using spherical harmonics and can be applied in those cases where the solar motion cannot be eliminated from the stellar proper motions. Numerical experiments have shown that our method is able to obtain accurate coordinates of the solar apex and to calculate the kinematic parameters of the Ogorodnikov-Milne model to within three coefficients of the decomposition of parallaxes into first-order spherical harmonics. Examples of applying the method to the stellar proper motions of the Hipparcos catalogue, which admits checking the results using trigonometric parallaxes, are provided. Such a check has been found to yield a positive result only for nearby stars at heliocentric distances that do not exceed 400 pc and for which the parallaxes were determined with a relative error of at least 30%. An interesting feature of this method is the possibility to construct the shape of the figure which is formed by the deviations of the parallaxes from the Sphere corresponding to the average parallaxes of the stars under consideration. It should be specially emphasized that all of this is done in the complete absence of information about the stellar parallaxes. The “solar terms” of the stellar proper motions that are formed by the products of the parallaxes by the solar motion components relative to the centroid of stars are the main source of information about the parallaxes here.
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Distortion of the stellar velocity field parameters due to systematic variations of parallaxes over the Celestial Sphere
Astronomy Letters, 2014Co-Authors: V. V. Vityazev, A. S. TsvetkovAbstract:We study the effect of systematic variations in stellar parallaxes over the Celestial Sphere on the results of a kinematic analysis of stellar proper motions. Our approach is based on the representation of stellar parallaxes by scalar spherical harmonics and on the decomposition of stellar proper motions into a system of vector spherical harmonics. We derive theoretical relations that relate the coefficients of the decomposition of stellar proper motions into toroidal and spheroidal harmonics to the coefficients of the decomposition of stellar parallaxes into scalar spherical harmonics. We have established that the systematic variations of parallaxes over the Celestial Sphere distort all parameters of the linear Ogorodnikov-Milne model and can be responsible for the appearance of beyond-the-model harmonics. We have performed a kinematic analysis of the proper motions of blue-white and red giants based on Hipparcos data. The parallaxes of blue-white giants show a strong dependence on Galactic latitude (with predominant contraction along the Galactic equator). In contrast, the deviations of the parallaxes from the mean for red giants are localized only in two regions of the Celestial Sphere. For these samples, the effect of parallax variations over the Celestial Sphere on kinematic parameters has turned out to be comparable to their rms errors. The global solutions performed using both samples have revealed strong beyond-the-model kinematic effects described by second-order toroidal harmonics and third-order spheroidal harmonics. Using the solutions performed separately in the northern and southern Galactic hemiSpheres, we have established that not the systematic variations of parallaxes over the Celestial Sphere but the retardation of Galactic rotation with increasing distance of stars from the principal Galactic plane is mainly responsible for the appearance of these harmonics. Based on these samples of stars, we have estimated the magnitude of the vertical Galactic rotation velocity gradient to be 18.0±2.9 and 22.7±2.2 km s−1 kpc−1, respectively.