scholarly journals Higher spin 3-point functions in 3d CFT using spinor-helicity variables

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Sachin Jain ◽  
Renjan Rajan John ◽  
Abhishek Mehta ◽  
Amin A. Nizami ◽  
Adithya Suresh
Keyword(s):  
Momentum Space ◽  
Conformally Invariant ◽  
Helicity Formalism ◽  
Higher Spin ◽  
Weight Shifting ◽  
Conserved Currents

Abstract In this paper we use the spinor-helicity formalism to calculate 3-point functions involving scalar operators and spin-s conserved currents in general 3d CFTs. In spinor-helicity variables we notice that the parity-even and the parity-odd parts of a correlator are related. Upon converting spinor-helicity answers to momentum space, we show that correlators involving spin-s currents can be expressed in terms of some simple conformally invariant conserved structures. This in particular allows us to understand and separate out contact terms systematically, especially for the parity-odd case. We also reproduce some of the correlators using weight-shifting operators.

Higher spin conserved currents in c = 1 conformally invariant systems

1988 ◽  
Vol 300 ◽  
pp. 637-657 ◽  
Author(s):  
M. Baake ◽  
P. Christe ◽  
V. Rittenberg
Keyword(s):  
Conformally Invariant ◽  
Higher Spin ◽  
Conserved Currents

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 Characteristic cohomology and observables in higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexey Sharapov ◽  
Evgeny Skvortsov
Keyword(s):  
Higher Spin Gravity ◽  
Complete Classification ◽  
Gravity Models ◽  
Simons Theory ◽  
Surface Charges ◽  
Higher Spin ◽  
Dynamical Invariants ◽  
Chern Simons ◽  
Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

scholarly journals The quantum one loop trace anomaly of the higher spin conformal conserved currents in the bulk of

2006 ◽  
Vol 733 (1-2) ◽  
pp. 104-122 ◽  
Author(s):  
Ruben Manvelyan ◽  
Werner Rühl
Keyword(s):  
Trace Anomaly ◽  
Higher Spin ◽  
Conserved Currents

scholarly journals Momentum space conformal three-point functions of conserved currents and a general spinning operator

2019 ◽  
Vol 2019 (5) ◽  
Author(s):  
Hiroshi Isono ◽  
Toshifumi Noumi ◽  
Toshiaki Takeuchi
Keyword(s):  
Momentum Space ◽  
Conserved Currents

scholarly journals UNFOLDED FORM OF CONFORMAL EQUATIONS IN M DIMENSIONS AND 𝔬(M + 2)-MODULES

2006 ◽  
Vol 18 (08) ◽  
pp. 823-886 ◽  
Author(s):  
O. V. SHAYNKMAN ◽  
I. YU. TIPUNIN ◽  
M. A. VASILIEV
Keyword(s):  
Differential Equations ◽  
Global Symmetry ◽  
Parabolic Subalgebra ◽  
Dynamical Equations ◽  
Conformally Invariant ◽  
Starting Point ◽  
Higher Spin ◽  
Symmetry Transformations ◽  
Invariant Differential ◽  
Linear Differential

A constructive procedure is proposed for formulation of linear differential equations invariant under global symmetry transformations forming a semi-simple Lie algebra 𝔣. Under certain conditions, 𝔣-invariant systems of differential equations are shown to be associated with 𝔣-modules that are integrable with respect to some parabolic subalgebra of 𝔣. The suggested construction is motivated by the unfolded formulation of dynamical equations developed in the higher spin gauge theory and provides a starting point for generalization to the nonlinear case. It is applied to the conformal algebra 𝔬(M, 2) to classify all linear conformally invariant differential equations in the Minkowski space. Numerous examples of conformal equations are discussed from this perspective.

Construction of conformally invariant higher spin operators using transvector algebras

2014 ◽  
Vol 55 (10) ◽  
pp. 101703 ◽  
Author(s):  
D. Eelbode ◽  
T. Raeymaekers
Keyword(s):  
Conformally Invariant ◽  
Higher Spin

Momentum space calculations and helicity formalism in nuclear physics

1971 ◽  
Vol 176 (2) ◽  
pp. 413-432 ◽  
Author(s):  
K. Erkelenz ◽  
R. Alzetta ◽  
K. Holinde
Keyword(s):  
Momentum Space ◽  
Nuclear Physics ◽  
Helicity Formalism

Structures of conserved currents and mass spectra for scalar fields. III. Current classification scheme in terms of Killing equations and the Goldstone theorem

1981 ◽  
Vol 59 (11) ◽  
pp. 1680-1681
Author(s):  
Meiun Shintani
Keyword(s):  
Mass Spectra ◽  
Classification Scheme ◽  
Goldstone Boson ◽  
Scalar Fields ◽  
Conformal Transformations ◽  
Goldstone Theorem ◽  
Scalar Particles ◽  
Conformally Invariant ◽  
Conserved Currents ◽  
Killing Equations

We present a new classification scheme for the currents Jμ(x) = Qμν(x)Cν(x) in terms of the solutions of the Killing equations for Cμ(x). The new scheme enables us to treat any coordinate transformations (e.g., special conformal transformations), and to discuss the mass spectra for the scalar particles in a conformally-invariant system. Moreover, with the aid of the generalized Goldstone theorem exploited in the previous article under the same title, we shall point out the nonexistence of the Goldstone boson with regard to the special conformal transformations.

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