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.

Ward Identities for W ∞ , Conformal Field Theories on a Torus

1991 ◽  
Vol 16 (4) ◽  
pp. 493-496
Author(s):  
Chao-Shang Huang ◽  
Liang-Xin Li ◽  
De-Hai Zhang
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Ward Identities ◽  
Conformal Field

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 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.

THE TODA LATTICE HIERARCHY AND DEFORMATIONS OF CONFORMAL FIELD THEORIES

1990 ◽  
Vol 05 (07) ◽  
pp. 509-518 ◽  
Author(s):  
MASAFUMI FUKUMA ◽  
TAKASHI TAKEBE
Keyword(s):  
Toda Lattice ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Kp Hierarchy ◽  
Soliton Theory ◽  
Conformal Field ◽  
Perturbed System ◽  
Conserved Currents ◽  
Toda Lattice Hierarchy

We point out that the Toda lattice hierarchy known in soliton theory is relevant for the description of the deformations of conformal field theories while the KP hierarchy describes unperturbed conformal theories. It is shown that the holomorphic parts of the conserved currents in the perturbed system (the Toda lattice hierarchy) coincide with the conserved currents in the KP hierarchy and can be written in terms of the W-algebraic currents. Furthermore, their anti-holomorphic counterparts are obtained.

scholarly journals Recursion relations for 5-point conformal blocks

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
David Poland ◽  
Valentina Prilepina
Keyword(s):  
Linear Combination ◽  
Energy Operator ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Point Function ◽  
Conformal Blocks ◽  
Recursion Relations ◽  
Expectation Value ◽  
Conformal Field ◽  
Weight Shifting

Abstract We consider 5-point functions in conformal field theories in d > 2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of scalar operators, reducing them to a linear combination of blocks with scalars exchanged. We additionally derive recursion relations for the conformal blocks which appear when one of the external operators in the 5-point function has spin 1 or 2. Our results allow us to formulate positivity constraints using 5-point functions which describe the expectation value of the energy operator in bilocal states created by two scalars.

scholarly journals Conformal Ward Identities and the Coupling of QED and QCD to Gravity

2018 ◽  
Vol 192 ◽  
pp. 00047
Author(s):  
Claudio Corianò ◽  
Matteo Maria Maglio
Keyword(s):  
Field Theory ◽  
Momentum Space ◽  
Free Field ◽  
Field Theories ◽  
Conformal Anomaly ◽  
Reconstruction Method ◽  
General Study ◽  
Ward Identities ◽  
Conformal Field ◽  
Flat Background

We present a general study of 3-point functions of conformal field theory (CFT) in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWIs), introduced in recent works. We investigate and detail the structure of the CWIs and their non-perturbative solutions, and compare them to perturbation theory, taking QED and QCD as examples. Exact solutions of CFT’s in the flat background limit in momentum space are matched by the perturbative realizations in free field theories, showing that the origin the conformal anomaly is related to effective scalar interactions, generated by the renormalization of the longitudinal components of the corresponding operators.

scholarly journals PROBING UNIVERSALITY IN AdS/CFT

2010 ◽  
Vol 25 (02n03) ◽  
pp. 433-443 ◽  
Author(s):  
A. RITZ
Keyword(s):  
Transport Coefficients ◽  
De Sitter Space ◽  
Field Theories ◽  
Conformal Field Theories ◽  
De Sitter ◽  
Thermodynamic State ◽  
Conformal Field ◽  
Large N ◽  
Conserved Currents ◽  
State Functions

We discuss some universal relations that hold for conformal field theories which admit a dual classical gravitational description in anti-de Sitter space. These relations therefore apply in a suitable large N limit, and imply that various hydrodynamic transport coefficients for conserved currents and thermodynamic state functions are entirely fixed by central charges.

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

Sign in / Sign up

Export Citation Format

Share Document