scholarly journals Double copy structure of parity-violating CFT correlators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Sachin Jain ◽  
Renjan Rajan John ◽  
Abhishek Mehta ◽  
Amin A. Nizami ◽  
Adithya Suresh
Keyword(s):  
Flat Space ◽  
Field Theories ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Spin ◽  
Space Limit ◽  
Double Copy ◽  
Conserved Currents ◽  
Massless Fields

Abstract We show that general parity-violating 3d conformal field theories show a double copy structure for momentum space 3-point functions of conserved currents, stress tensor and marginal scalar operators. Splitting up the CFT correlator into two parts — called homogeneous and non-homogeneous — we show that double copy relations exist for each part separately. We arrive at similar conclusions regarding double copy structures using tree-level correlators of massless fields in dS4. We also discuss the flat space limit of these correlators. We further extend the double copy analysis to correlators involving higher-spin conserved currents, which suggests that the spin-s current correlator can be thought of as s copies of the spin one current correlator.

scholarly journals CFT unitarity and the AdS Cutkosky rules

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
David Meltzer ◽  
Allic Sivaramakrishnan
Keyword(s):  
Flat Space ◽  
Tree Level ◽  
Optical Theorem ◽  
Conformal Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Weakly Coupled ◽  
S Matrix ◽  
Space Limit ◽  
Diagrammatic Method

Abstract We derive the Cutkosky rules for conformal field theories (CFTs) at weak and strong coupling. These rules give a simple, diagrammatic method to compute the double-commutator that appears in the Lorentzian inversion formula. We first revisit weakly-coupled CFTs in flat space, where the cuts are performed on Feynman diagrams. We then generalize these rules to strongly-coupled holographic CFTs, where the cuts are performed on the Witten diagrams of the dual theory. In both cases, Cutkosky rules factorize loop diagrams into on-shell sub-diagrams and generalize the standard S-matrix cutting rules. These rules are naturally formulated and derived in Lorentzian momentum space, where the double-commutator is manifestly related to the CFT optical theorem. Finally, we study the AdS cutting rules in explicit examples at tree level and one loop. In these examples, we confirm that the rules are consistent with the OPE limit and that we recover the S-matrix optical theorem in the flat space limit. The AdS cutting rules and the CFT dispersion formula together form a holographic unitarity method to reconstruct Witten diagrams from their cuts.

scholarly journals The Schwarzian sector of higher spin CFTs

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Shouvik Datta
Keyword(s):  
Spectral Decomposition ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Btz Black Hole ◽  
Conformal Field ◽  
Virasoro Symmetry ◽  
Higher Spin ◽  
Extremal Limit ◽  
Conserved Currents

Abstract Two-dimensional conformal field theories with Virasoro symmetry generically contain a Schwarzian sector. This sector is related to the near-horizon region of the near-extremal BTZ black hole in the holographic dual. In this work we generalize this picture to CFTs with higher spin conserved currents. It is shown that the partition function in the near-extremal limit agrees with that of BF higher spin gravity in AdS2 which is described by a generalized Schwarzian theory. We also provide a spectral decomposition of Schwarzian partition functions via the $$ {\mathcal{W}}_N $$ W N fusion kernel and consider supersymmetric generalizations.

scholarly journals Momentum space parity-odd CFT 3-point functions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Sachin Jain ◽  
Renjan Rajan John ◽  
Abhishek Mehta ◽  
Amin A. Nizami ◽  
Adithya Suresh
Keyword(s):  
Momentum Space ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Ward Identities ◽  
Conformal Field ◽  
Weight Shifting ◽  
Conserved Currents

Abstract We study the parity-odd sector of 3-point functions comprising scalar operators and conserved currents in conformal field theories in momentum space. We use momentum space conformal Ward identities as well as spin-raising and weight-shifting operators to fix the form of some of these correlators. Wherever divergences appear we discuss their regularisation and renormalisation using appropriate counter-terms.

scholarly journals Helicity basis for three-dimensional conformal field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Simon Caron-Huot ◽  
Yue-Zhou Li
Keyword(s):  
Conformal Symmetry ◽  
Mean Field ◽  
Three Dimensional ◽  
Flat Space ◽  
Three Dimensions ◽  
Tree Level ◽  
Conformal Field ◽  
Anomalous Dimensions ◽  
Conserved Currents ◽  
Level Order

Abstract Three-point correlators of spinning operators admit multiple tensor structures compatible with conformal symmetry. For conserved currents in three dimensions, we point out that helicity commutes with conformal transformations and we use this to construct three-point structures which diagonalize helicity. In this helicity basis, OPE data is found to be diagonal for mean-field correlators of conserved currents and stress tensor. Furthermore, we use Lorentzian inversion formula to obtain anomalous dimensions for conserved currents at bulk tree-level order in holographic theories, which we compare with corresponding flat-space gluon scattering amplitudes.

scholarly journals Two-photon processes in conformal QCD: resummation of the descendants of leading-twist operators

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
V.M. Braun ◽  
Yao Ji ◽  
A.N. Manashov
Keyword(s):  
Deeply Virtual Compton Scattering ◽  
Virtual Compton Scattering ◽  
Field Theories ◽  
Tree Level ◽  
Operator Product ◽  
Conformal Field Theories ◽  
Closed Expression ◽  
Conformal Field ◽  
Two Photon ◽  
Twist Operators

Abstract Using some techniques of conformal field theories, we find a closed expression for the contribution of leading twist operators and their descendants, obtained by adding total derivatives, to the operator product expansion (OPE) of two electromagnetic currents in QCD. Our expression resums contributions of all twists and to all orders in perturbation theory up to corrections proportional to the QCD β-function. At tree level and to twist-four accuracy, our result agrees with the expression derived earlier by a different method. The results are directly applicable to deeply-virtual Compton scattering and, e.g., γγ∗ annihilation in two mesons. As a byproduct, we derive a simple representation for the OPE of two scalar currents that is convenient for applications.

scholarly journals Applications of dispersive sum rules: $ε$-expansion and holography

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Dean Carmi ◽  
Joao Penedones ◽  
Joao A. Silva ◽  
Alexander Zhiboedov
Keyword(s):  
Sum Rules ◽  
Dispersion Relations ◽  
Field Theories ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Anomalous Dimensions ◽  
Fisher Model ◽  
Twist Operators ◽  
Space Dispersion

We use Mellin space dispersion relations together with Polyakov conditions to derive a family of sum rules for Conformal Field Theories (CFTs). The defining property of these sum rules is suppression of the contribution of the double twist operators. Firstly, we apply these sum rules to the Wilson-Fisher model in d=4-\epsilond=4−ϵ dimensions. We re-derive many of the known results to order \epsilon^4ϵ4 and we make new predictions. No assumption of analyticity down to spin 00 was made. Secondly, we study holographic CFTs. We use dispersive sum rules to obtain tree-level and one-loop anomalous dimensions. Finally, we briefly discuss the contribution of heavy operators to the sum rules in UV complete holographic theories.

scholarly journals GELFAND–DICKEY ALGEBRA AND HIGHER SPIN SYMMETRIES ON T2 = S1 × S1

2008 ◽  
Vol 23 (31) ◽  
pp. 5059-5080
Author(s):  
M. B. SEDRA
Keyword(s):  
Integrable Models ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Dimensional Torus ◽  
Conformal Field ◽  
Generalized Symmetries ◽  
Higher Spin

In this work we aim to renew the interest in higher conformal spins symmetries and their relations to quantum field theories and integrable models. We consider the extension of the conformal Frappat et al. symmetries containing the Virasoro and the Antoniadis et al. algebras as particular cases describing geometrically special diffeomorphisms of the two-dimensional torus T2. We show explicitly, in a consistent way, how one can extract these generalized symmetries from the Gelfand–Dickey algebra. The link with Liouville and Toda conformal field theories is established and various important properties are discussed.

Sign in / Sign up

Export Citation Format

Share Document