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Andrei Parnachev - One of the best experts on this subject based on the ideXlab platform.
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Stress Tensor Sector of Conformal Correlators
arXiv: High Energy Physics - Theory, 2020Co-Authors: Robin Karlsson, Manuela Kulaxizi, Andrei Parnachev, Petar TadićAbstract:An important part of a CFT four-point function, the Stress tensor sector, comprises the exchanges of the Stress tensor and its composites. The OPE coefficients of these multi-Stress tensor operators and consequently, the complete Stress tensor sector of four-point functions in CFTs with a large central charge, can be determined by computing a heavy-heavy-light-light correlator. We show how one can make substantial progress in this direction by bootstrapping a certain ansatz for the Stress tensor sector of the correlator, iteratively computing the OPE coefficients of multi-Stress tensor operators with increasing twist. Some parameters are not fixed by the bootstrap - they correspond to the OPE coefficients of multi-Stress Tensors with spin zero and two. We further show that in holographic CFTs one can use the phase shift computed in the dual gravitational theory to reduce the set of undetermined parameters to the OPE coefficients of multi-Stress Tensors with spin zero. Finally, we verify some of these results using the Lorentzian OPE inversion formula and comment on its regime of applicability.
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leading multi Stress Tensors and conformal bootstrap
Journal of High Energy Physics, 2020Co-Authors: Robin Karlsson, Manuela Kulaxizi, Andrei Parnachev, Petar TadicAbstract:Near lightcone correlators are dominated by operators with the lowest twist. We consider the contributions of such leading lowest twist multi-Stress tensor operators to a heavy-heavy-light-light correlator in a CFT of any even dimensionality with a large central charge. An infinite number of such operators contribute, but their sum is described by a simple ansatz. We show that the coefficients in this ansatz can be determined recursively, thereby providing an operational procedure to compute them. This is achieved by bootstrapping the corresponding near lightcone correlator: conformal data for any minimal twist determines that for the higher minimal-twist and so on. To illustrate this procedure in four spacetime dimensions we determine the contributions of double- and triple-Stress Tensors. We compute the OPE coefficients; whenever results are available in the literature, we observe complete agreement. We also compute the contributions of double-Stress Tensors in six spacetime dimensions and determine the corresponding OPE coefficients. In all cases the results are consistent with the exponentiation of the near lightcone correlator. This is similar to the situation in two spacetime dimensions for the Virasoro vacuum block.
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Subleading Eikonal, AdS/CFT and Double Stress Tensors
Journal of High Energy Physics, 2019Co-Authors: Manuela Kulaxizi, Andrei ParnachevAbstract:The eikonal phase which determines the Regge limit of the gravitational scattering amplitude of a light particle off a heavy one in Minkowski spacetimes admits an expansion in the ratio of the Schwarzschild radius of the heavy particle to the impact parameter. Such an eikonal phase in AdS spacetimes of any dimensionality has been computed to all orders and reduces to the corresponding Minkowski result when both the impact parameter and the Schwarzschild radius are much smaller than the AdS radius. The leading term in the AdS eikonal phase can be reproduced in the dual CFT by a single Stress tensor conformal block, but the subleading term is a result of an infinite sum of the double Stress tensor contributions. We provide a closed form expression for the OPE coefficients of the leading twist double Stress Tensors in four spacetime dimensions and perform the sum to compute the corresponding lightcone behavior of a heavy-heavy-light-light CFT correlator. The resulting compact expression passes a few nontrivial independent checks. In particular, it agrees with the subleading eikonal phase at large impact parameter.
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subleading eikonal ads cft and double Stress Tensors
Journal of High Energy Physics, 2019Co-Authors: Manuela Kulaxizi, Andrei ParnachevAbstract:The eikonal phase which determines the Regge limit of the gravitational scat- tering amplitude of a light particle off a heavy one in Minkowski spacetimes admits an expansion in the ratio of the Schwarzschild radius of the heavy particle to the impact parameter. Such an eikonal phase in AdS spacetimes of any dimensionality has been com- puted to all orders and reduces to the corresponding Minkowski result when both the impact parameter and the Schwarzschild radius are much smaller than the AdS radius. The leading term in the AdS eikonal phase can be reproduced in the dual CFT by a single Stress tensor conformal block, but the subleading term is a result of an infinite sum of the double Stress tensor contributions. We provide a closed form expression for the OPE coef- ficients of the leading twist double Stress Tensors in four spacetime dimensions and perform the sum to compute the corresponding lightcone behavior of a heavy-heavy-light-light CFT correlator. The resulting compact expression passes a few nontrivial independent checks. In particular, it agrees with the subleading eikonal phase at large impact parameter.
Manuela Kulaxizi - One of the best experts on this subject based on the ideXlab platform.
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Stress Tensor Sector of Conformal Correlators
arXiv: High Energy Physics - Theory, 2020Co-Authors: Robin Karlsson, Manuela Kulaxizi, Andrei Parnachev, Petar TadićAbstract:An important part of a CFT four-point function, the Stress tensor sector, comprises the exchanges of the Stress tensor and its composites. The OPE coefficients of these multi-Stress tensor operators and consequently, the complete Stress tensor sector of four-point functions in CFTs with a large central charge, can be determined by computing a heavy-heavy-light-light correlator. We show how one can make substantial progress in this direction by bootstrapping a certain ansatz for the Stress tensor sector of the correlator, iteratively computing the OPE coefficients of multi-Stress tensor operators with increasing twist. Some parameters are not fixed by the bootstrap - they correspond to the OPE coefficients of multi-Stress Tensors with spin zero and two. We further show that in holographic CFTs one can use the phase shift computed in the dual gravitational theory to reduce the set of undetermined parameters to the OPE coefficients of multi-Stress Tensors with spin zero. Finally, we verify some of these results using the Lorentzian OPE inversion formula and comment on its regime of applicability.
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leading multi Stress Tensors and conformal bootstrap
Journal of High Energy Physics, 2020Co-Authors: Robin Karlsson, Manuela Kulaxizi, Andrei Parnachev, Petar TadicAbstract:Near lightcone correlators are dominated by operators with the lowest twist. We consider the contributions of such leading lowest twist multi-Stress tensor operators to a heavy-heavy-light-light correlator in a CFT of any even dimensionality with a large central charge. An infinite number of such operators contribute, but their sum is described by a simple ansatz. We show that the coefficients in this ansatz can be determined recursively, thereby providing an operational procedure to compute them. This is achieved by bootstrapping the corresponding near lightcone correlator: conformal data for any minimal twist determines that for the higher minimal-twist and so on. To illustrate this procedure in four spacetime dimensions we determine the contributions of double- and triple-Stress Tensors. We compute the OPE coefficients; whenever results are available in the literature, we observe complete agreement. We also compute the contributions of double-Stress Tensors in six spacetime dimensions and determine the corresponding OPE coefficients. In all cases the results are consistent with the exponentiation of the near lightcone correlator. This is similar to the situation in two spacetime dimensions for the Virasoro vacuum block.
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Subleading Eikonal, AdS/CFT and Double Stress Tensors
Journal of High Energy Physics, 2019Co-Authors: Manuela Kulaxizi, Andrei ParnachevAbstract:The eikonal phase which determines the Regge limit of the gravitational scattering amplitude of a light particle off a heavy one in Minkowski spacetimes admits an expansion in the ratio of the Schwarzschild radius of the heavy particle to the impact parameter. Such an eikonal phase in AdS spacetimes of any dimensionality has been computed to all orders and reduces to the corresponding Minkowski result when both the impact parameter and the Schwarzschild radius are much smaller than the AdS radius. The leading term in the AdS eikonal phase can be reproduced in the dual CFT by a single Stress tensor conformal block, but the subleading term is a result of an infinite sum of the double Stress tensor contributions. We provide a closed form expression for the OPE coefficients of the leading twist double Stress Tensors in four spacetime dimensions and perform the sum to compute the corresponding lightcone behavior of a heavy-heavy-light-light CFT correlator. The resulting compact expression passes a few nontrivial independent checks. In particular, it agrees with the subleading eikonal phase at large impact parameter.
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subleading eikonal ads cft and double Stress Tensors
Journal of High Energy Physics, 2019Co-Authors: Manuela Kulaxizi, Andrei ParnachevAbstract:The eikonal phase which determines the Regge limit of the gravitational scat- tering amplitude of a light particle off a heavy one in Minkowski spacetimes admits an expansion in the ratio of the Schwarzschild radius of the heavy particle to the impact parameter. Such an eikonal phase in AdS spacetimes of any dimensionality has been com- puted to all orders and reduces to the corresponding Minkowski result when both the impact parameter and the Schwarzschild radius are much smaller than the AdS radius. The leading term in the AdS eikonal phase can be reproduced in the dual CFT by a single Stress tensor conformal block, but the subleading term is a result of an infinite sum of the double Stress tensor contributions. We provide a closed form expression for the OPE coef- ficients of the leading twist double Stress Tensors in four spacetime dimensions and perform the sum to compute the corresponding lightcone behavior of a heavy-heavy-light-light CFT correlator. The resulting compact expression passes a few nontrivial independent checks. In particular, it agrees with the subleading eikonal phase at large impact parameter.
Kostas Skenderis - One of the best experts on this subject based on the ideXlab platform.
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renormalised 3 point functions of Stress Tensors and conserved currents in cft
Journal of High Energy Physics, 2018Co-Authors: Adam Bzowski, Paul Mcfadden, Kostas SkenderisAbstract:We present a complete momentum-space prescription for the renormalisation of tensorial correlators in conformal field theories. Our discussion covers all 3-point functions of Stress Tensors and conserved currents in arbitrary spacetime dimensions. In dimensions three and four, we give explicit results for the renormalised correlators, the anomalous Ward identities they obey, and the conformal anomalies. For the Stress tensor 3-point function in four dimensions, we identify the specific evanescent tensorial structure responsible for the type A Euler anomaly, and show this anomaly has the form of a double copy of the chiral anomaly.
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renormalised cft 3 point functions of scalars currents and Stress Tensors
arXiv: High Energy Physics - Theory, 2018Co-Authors: Adam Bzowski, Paul Mcfadden, Kostas SkenderisAbstract:We discuss the renormalisation of mixed 3-point functions involving tensorial and scalar operators in conformal field theories of general dimension. In previous work we analysed correlators of either purely scalar or purely tensorial operators, in each case finding new features and new complications: for scalar correlators, renormalisation leads to beta functions, novel conformal anomalies of type B, and unexpected analytic structure in momentum space; for correlators of Stress Tensors and/or conserved currents, beta functions vanish but anomalies of both type B and type A (associated with a $0/0$ structure) are present. Mixed correlators combine all these features: beta functions and anomalies of type B, plus the possibility of new type A anomalies. Following a non-perturbative and general momentum-space analysis, we present explicit results in dimensions $d=3,4$ for all renormalised 3-point functions of Stress Tensors, conserved currents and scalars of dimensions $\Delta=d$ and $\Delta=d-2$. We identify all anomalies and beta functions, and explain the form of the anomalous conformal Ward identities. In $d=3$, we find a $0/0$ structure but the corresponding type A anomaly turns out to be trivial. In addition, the correlators of two currents and a scalar, and of two Stress Tensors and a scalar, both feature universal tensor structures that are independent of the scalar dimension and vanish for opposite helicities.
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Renormalised CFT 3-point functions of scalars, currents and Stress Tensors
JHEP, 2018Co-Authors: Adam Bzowski, Paul Mcfadden, Kostas SkenderisAbstract:We discuss the renormalisation of mixed 3-point functions involving tensorial and scalar operators in conformal field theories of general dimension. In previous work we analysed correlators of either purely scalar or purely tensorial operators, in each case finding new features and new complications: for scalar correlators, renormalisation leads to beta functions, novel conformal anomalies of type B, and unexpected analytic structure in momentum space, for correlators of Stress Tensors and/or conserved currents, beta functions vanish but anomalies of both type B and type A (associated with a 0/0 structure) are present. Mixed correlators combine all these features: beta functions and anomalies of type B, plus the possibility of new type A anomalies. Following a non-perturbative and general momentum-space analysis, we present explicit results in dimensions d = 3, 4 for all renormalised 3-point functions of Stress Tensors, conserved currents and scalars of dimensions Δ = d and Δ = d − 2. We identify all anomalies and beta functions, and explain the form of the anomalous conformal Ward identities. In d = 3, we find a 0/0 structure but the corresponding type A anomaly turns out to be trivial. In addition, the correlators of two currents and a scalar, and of two Stress Tensors and a scalar, both feature universal tensor structures that are independent of the scalar dimension and vanish for opposite helicities.
John Moore - One of the best experts on this subject based on the ideXlab platform.
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Education Committee Best Paper of 1995 Award: Methods of Classical Mechanics Applied to Turbulence Stresses in a Tip Leakage Vortex
Journal of Turbomachinery, 1996Co-Authors: Joan G. Moore, S. A. Schorn, John MooreAbstract:Moore et al. measured the six Reynolds Stresses in a tip leakage vortex in a linear turbine cascade. Stress tensor analysis, as used in classical mechanics, has been applied to the measured turbulence Stress Tensors. Principal directions and principal normal Stresses are found. A solid surface model, or three-dimensional glyph, for the Reynolds Stress tensor is proposed and used to view the Stresses throughout the tip leakage vortex. Modeled Reynolds Stresses using the Boussinesq approximation are obtained from the measured mean velocity strain rate tensor. The comparison of the principal directions and the three-dimensional graphic representations of the strain and Reynolds Stress Tensors aids in the understanding of the turbulence and what is required to model it.
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Methods of Classical Mechanics Applied to Turbulence Stresses in a Tip Leakage Vortex
Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls Diagnostics and Instrumentation; Education; IGTI Scholar, 1995Co-Authors: Joan G. Moore, S. A. Schorn, John MooreAbstract:Moore et al. measured the six Reynolds Stresses in a tip leakage vortex in a linear turbine cascade. Stress tensor analysis, as used in classical mechanics, has been applied to the measured turbulence Stress Tensors. Principal directions and principal normal Stresses are found. A solid surface model, or 3-d glyph, for the Reynolds Stress tensor is proposed and used to view the Stresses throughout the tip leakage vortex. Modelled Reynolds Stresses using the Boussinesq approximation are obtained from the measured mean velocity strain rate tensor. The comparison of the principal directions and the 3-d graphical representations of the strain and Reynolds Stress Tensors aids in the understanding of the turbulence and what is required to model it.Copyright © 1995 by ASME
Reza Naghdabadi - One of the best experts on this subject based on the ideXlab platform.
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Intrinsic Expressions for Arbitrary Stress Tensors Conjugate to General Strain Tensors
Scientia Iranica, 2007Co-Authors: Saeed Sohrabpour, Mohsen Asghari, Reza NaghdabadiAbstract:In this paper, a uni ed explicit tensorial relation is sought between two Stress Tensors conjugate to arbitrary and general Hill strains. The approach used for deriving the tensorial relation is based on the eigenprojection method. The result is, indeed, a generalization of the relations that were derived by Farahani and Naghadabadi [1] in 2003 from a component to intrinsic form. The result is uni ed in the sense that it is valid for all cases of distinct and coalescent principal stretches. Also, in the case of three dimensional Euclidean inner product space, using the derived uni ed relation, some expressions for the conjugate Stress Tensors are presented.
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Basis-free relations for conjugate strains of Eshelby-like Stress Tensors
Mechanics of Materials, 2007Co-Authors: K. Behfar, Reza Naghdabadi, J. Arghavani, Mohsen AsghariAbstract:Abstract In this paper, a general class of Eshelby-like or weighted Stress Tensors based on the right stretch tensor is defined as the product of a general type of Lagrangian Stress tensor and a class of stretch measure. In addition, basis free relations for conjugate strains of Eshelby-like Stress Tensors are investigated, which are based on Hill’s definition of energy conjugacy. The equations for strain Tensors conjugate to Eshelby-like Stress Tensors are generally determined, but the case in which the conjugate strains are coaxial with the right stretch tensor is mostly investigated.
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General Derivations for Conjugate Strains of Eshelby-Like Stress Tensors
Volume!, 2004Co-Authors: K. Behfar, A. Sheshmani, Reza NaghdabadiAbstract:In this paper, a general type of Eshelby-like Stress tensor is defined which is based on the right stretch tensor and is equal to the product of a general class of strain and the corresponding conjugate Stress tensor. The Eshelby-like Stress tensor depending on the fact that from which side the Stress tensor is multiplied by, is categorized into the right-weighted and left-weighted ones. General relations for conjugate strains of Eshelby-like Stress Tensors are investigated using the method, based on the definition of energy conjugacy and Hill’s principal axis method.Copyright © 2004 by ASME
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Conjugate Stresses of the Seth–Hill strain Tensors
International Journal of Solids and Structures, 2000Co-Authors: K. Farahani, Reza NaghdabadiAbstract:Abstract In this paper, conjugate Stresses of the Seth–Hill strain measures are treated by means of the definition of energy conjugacy and Hill’s principal axis method. This approach results in relations between components of two different conjugate Stress Tensors. The results are valid for distinct as well as coalescent principal stretches. Illustrative examples are solved to demonstrate the simplicity and usefulness of the derived relations between conjugate Stress Tensors.