scholarly journals More on heavy-light bootstrap up to double-stress-tensor

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Yue-Zhou Li ◽  
Hao-Yu Zhang
Keyword(s):  
Stress Tensor ◽  
Inversion Formula ◽  
Anomalous Dimension ◽  
Point Function ◽  
Regge Behavior ◽  
General Dimension ◽  
Stress Tensors ◽  
Anomalous Dimensions ◽  
Large Impact Parameter ◽  
Twist Operators

Abstract We investigate the heavy-light four-point function up to double-stress-tensor, supplementing 1910.06357. By using the OPE coefficients of lowest-twist double-stress- tensor in the literature, we find the Regge behavior for lowest-twist double-stress-tensor in general even dimension within the large impact parameter regime. In the next, we perform the Lorentzian inversion formula to obtain both the OPE coefficients and anomalous dimensions of double-twist operators [$$ \mathcal{O} $$ O H$$ \mathcal{O} $$ O L]n,J with finite spin J in d = 4. We also extract the anomalous dimensions of double-twist operators with finite spin in general dimension, which allows us to address the cases that ∆L is specified to the poles in lowest-twist double-stress-tensors where certain double-trace operators [$$ \mathcal{O} $$ O L$$ \mathcal{O} $$ O L]n,J mix with lowest-twist double-stress-tensors. In particular, we verify and discuss the Residue relation that deter- mines the product of the mixed anomalous dimension and the mixed OPE. We also present the double-trace and mixed OPE coefficients associated with ∆L poles in d = 6, 8. In the end, we turn to discuss CFT2, we verify the uniqueness of double-stress-tensor that is consistent with Virasoso symmetry.

scholarly journals Regge trajectories for the (2, 0) theories

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Madalena Lemos ◽  
Balt C. van Rees ◽  
Xiang Zhao
Keyword(s):  
Stress Tensor ◽  
Inversion Formula ◽  
Numerical Experiments ◽  
Iterative Scheme ◽  
Point Function ◽  
Regge Trajectories ◽  
Regge Behavior ◽  
Six Dimensions ◽  
Tensor Multiplet

Abstract We investigate the structure of conformal Regge trajectories for the maximally supersymmetric (2, 0) theories in six dimensions. The different conformal multiplets in a single superconformal multiplet must all have similarly-shaped Regge trajectories. We show that these super-descendant trajectories interact in interesting ways, leading to new constraints on their shape. For the four-point function of the stress tensor multiplet supersymmetry also softens the Regge behavior in some channels, and consequently we observe that ‘analyticity in spin’ holds for all spins greater than −3. All the physical operators in this correlator therefore lie on Regge trajectories and we describe an iterative scheme where the Lorentzian inversion formula can be used to bootstrap the four-point function. Some numerical experiments yield promising results, with OPE data approaching the numerical bootstrap results for all theories with rank greater than one.

scholarly journals Two-point correlator of chiral primary operators with a Wilson line defect in $$ \mathcal{N} $$ = 4 SYM

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Julien Barrat ◽  
Pedro Liendo ◽  
Jan Plefka
Keyword(s):  
Closed Form ◽  
Stress Tensor ◽  
Wilson Line ◽  
Trace Operator ◽  
Line Defect ◽  
Point Function ◽  
Anomalous Dimensions ◽  
Tensor Multiplet ◽  
The One ◽  
Single Trace

Abstract We study the two-point function of the stress-tensor multiplet of $$ \mathcal{N} $$ N = 4 SYM in the presence of a line defect. To be more precise, we focus on the single-trace operator of conformal dimension two that sits in the 20′ irrep of the $$ \mathfrak{so} $$ so (6)R R-symmetry, and add a Maldacena-Wilson line to the configuration which makes the two-point function non-trivial. We use a combination of perturbation theory and defect CFT techniques to obtain results up to next-to-leading order in the coupling constant. Being a defect CFT correlator, there exist two (super)conformal block expansions which capture defect and bulk data respectively. We present a closed-form formula for the defect CFT data, which allows to write an efficient Taylor series for the correlator in the limit when one of the operators is close to the line. The bulk channel is technically harder and closed-form formulae are particularly challenging to obtain, nevertheless we use our analysis to check against well-known data of $$ \mathcal{N} $$ N = 4 SYM. In particular, we recover the correct anomalous dimensions of a famous tower of twist-two operators (which includes the Konishi multiplet), and successfully compare the one-point function of the stress-tensor multiplet with results obtained using matrix-model techniques.

scholarly journals Defect CFT techniques in the 6d $$ \mathcal{N} $$ = (2, 0) theory

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nadav Drukker ◽  
Malte Probst ◽  
Maxime Trépanier
Keyword(s):  
Stress Tensor ◽  
Unitary Representations ◽  
Point Function ◽  
Displacement Operator ◽  
Expectation Value ◽  
Operator Expansion ◽  
Bulk Stress ◽  
Defect Operator ◽  
Tensor Multiplet

Abstract Surface operators are among the most important observables of the 6d $$ \mathcal{N} $$ N = (2, 0) theory. Here we apply the tools of defect CFT to study local operator insertions into the 1/2-BPS plane. We first relate the 2-point function of the displacement operator to the expectation value of the bulk stress tensor and translate this relation into a constraint on the anomaly coefficients associated with the defect. Secondly, we study the defect operator expansion of the stress tensor multiplet and identify several new operators of the defect CFT. Technical results derived along the way include the explicit supersymmetry tranformations of the stress tensor multiplet and the classification of unitary representations of the superconformal algebra preserved by the defect.

scholarly journals Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, p-forms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Justin R. David ◽  
Jyotirmoy Mukherjee
Keyword(s):  
Stress Tensor ◽  
Entanglement Entropy ◽  
Partition Functions ◽  
Point Function ◽  
Expectation Value ◽  
Massive Spin ◽  
Twist Operator ◽  
Higher Spins ◽  
Hyperbolic Cylinders ◽  
Kaluza Klein

Abstract We show that the entanglement entropy of D = 4 linearized gravitons across a sphere recently computed by Benedetti and Casini coincides with that obtained using the Kaluza-Klein tower of traceless transverse massive spin-2 fields on S1× AdS3. The mass of the constant mode on S1 saturates the Brietenholer-Freedman bound in AdS3. This condition also ensures that the entanglement entropy of higher spins determined from partition functions on the hyperbolic cylinder coincides with their recent conjecture. Starting from the action of the 2-form on S1× AdS5 and fixing gauge, we evaluate the entanglement entropy across a sphere as well as the dimensions of the corresponding twist operator. We demonstrate that the conformal dimensions of the corresponding twist operator agrees with that obtained using the expectation value of the stress tensor on the replica cone. For conformal p-forms in even dimensions it obeys the expected relations with the coefficients determining the 3-point function of the stress tensor of these fields.

scholarly journals Mixed scalar-current bootstrap in three dimensions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Marten Reehorst ◽  
Emilio Trevisani ◽  
Alessandro Vichi
Keyword(s):  
Stress Tensor ◽  
Quantum Monte Carlo ◽  
Three Dimensions ◽  
Mixed System ◽  
Point Function ◽  
Function Coefficient ◽  
Rigorous Bounds ◽  
Usual Scalar ◽  
Scalar Singlet ◽  
Scalar Current

Abstract We study the mixed system of correlation functions involving a scalar field charged under a global U(1) symmetry and the associated conserved spin-1 current Jμ. Using numerical bootstrap techniques we obtain bounds on new observables not accessible in the usual scalar bootstrap. We then specialize to the O(2) model and extract rigorous bounds on the three-point function coefficient of two currents and the unique relevant scalar singlet, as well as those of two currents and the stress tensor. Using these results, and comparing with a quantum Monte Carlo simulation of the O(2) model conductivity, we give estimates of the thermal one-point function of the relevant singlet and the stress tensor. We also obtain new bounds on operators in various sectors.

Education Committee Best Paper of 1995 Award: Methods of Classical Mechanics Applied to Turbulence Stresses in a Tip Leakage Vortex

1996 ◽  
Vol 118 (4) ◽  
pp. 622-629 ◽  
Author(s):  
J. G. Moore ◽  
S. A. Schorn ◽  
J. Moore
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Surface Model ◽  
Reynolds Stresses ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Stress Tensors ◽  
Principal Directions

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.

scholarly journals BRANCHED POLYMERS ON BRANCHED POLYMERS

1996 ◽  
Vol 11 (29) ◽  
pp. 2361-2368
Author(s):  
BERGFINNUR DURHUUS ◽  
THORDUR JONSSON
Keyword(s):  
Phase Transition ◽  
Transition Point ◽  
Anomalous Dimension ◽  
Geometrical Structure ◽  
Branched Polymers ◽  
Statistical System ◽  
Point Function

We study an ensemble of branched polymers which are embedded on other branched polymers. This is a toy model which allows us to study explicitly and in detail the reaction of a statistical system to its underlying geometrical structure, a problem of interest in the study of the interaction of matter and quantized gravity. We find a phase transition at which the embedded polymers begin to cover the basis polymers. At the transition point the susceptibility exponent γ takes the value 3/4 and the two-point function develops an anomalous dimension 1/2.

scholarly journals The High Spin Expansion of Twist Sector Dimensions: The Planar𝒩=4Super Yang-Mills Theory

2010 ◽  
Vol 2010 ◽  
pp. 1-30 ◽  
Author(s):  
Davide Fioravanti ◽  
Marco Rossi
Keyword(s):  
High Spin ◽  
Gauge Theories ◽  
Anomalous Dimension ◽  
Yang Mills ◽  
Analysis Tools ◽  
Twist Operators ◽  
Super Yang Mills Theory

This review is devoted to collecting some results on the high spin expansion of (minimal) anomalous dimension. Thanks to the recent rationale on integrability, planar𝒩=4super Yang-Mills theory (or itsAdS5×S5string counterpart) represents a very practicable field. Here the attention will be restricted to its sector of twist operators, although the analysis tools are quite general (in integrable theories). Some structures and ideas turn out to be general also for other sectors or gauge theories.

TOWARDS A CONFORMAL QED4 WITH A NONVANISHING CURRENT 2-POINT FUNCTION

1988 ◽  
Vol 03 (04) ◽  
pp. 1023-1049 ◽  
Author(s):  
YASSEN S. STANEV ◽  
IVAN T. TODOROV
Keyword(s):  
Quantum Electrodynamics ◽  
Anomalous Dimension ◽  
Operator Product ◽  
Indefinite Metric ◽  
Conformal Invariant ◽  
Point Function ◽  
Four Dimensions ◽  
Conformally Invariant ◽  
Longitudinal Correlation ◽  
Electron Field

The possibility of constructing a conformally invariant model of spinor quantum electrodynamics (QED) in four dimensions involving an anomalous dimension of the electron field and a general indecomposable conformal law for the Maxwell field Fµν is studied within the local indefinite metric framework making systematic use of conformal operator product expansions (OPEs). It is demonstrated that the standard elementary conformal law for Fµν, which is known to yield a vanishing current-current 2-point function leads to a trivial theory. On the other hand, the conformal invariant 2-point function <Jμ(x1)Jν(x2)> (proportional to the second order perturbation theory expression in a massless QED) gives rise to a soluble conformal model involving [Formula: see text] and a vector field Vµ with longitudinal correlation function. The question whether the model can be extended to include Fµν (rather than its divergence) remains unresolved.

Methods of Classical Mechanics Applied to Turbulence Stresses in a Tip Leakage Vortex

1995 ◽  
Author(s):  
Joan G. Moore ◽  
Scott A. Schorn ◽  
John Moore
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Classical Mechanics ◽  
Surface Model ◽  
Strain Rate Tensor ◽  
Reynolds Stresses ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Stress Tensors ◽  
Principal Directions

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.

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