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 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 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.

scholarly journals Application of a momentum-space semi-locally regularized chiral potential to selected disintegration processes

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
V. Urbanevych ◽  
R. Skibiński ◽  
H. Witała ◽  
J. Golak ◽  
K. Topolnicki ◽  
...  
Keyword(s):  
Momentum Space ◽  
Chiral Potential

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

scholarly journals The Dirac Sea, T and C Symmetry Breaking, and the Spinor Vacuum of the Universe

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 124
Author(s):  
Vadim Monakhov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Symmetry Breaking ◽  
Momentum Space ◽  
Quantum Field ◽  
Conjugation Operator ◽  
Dirac Sea ◽  
Canonical Anticommutation Relations ◽  
The Universe ◽  
Dirac Conjugation

We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra) of Grassmann densities in the momentum space. We have proven the existence of two spinor vacua. Operators C and T transform the normal vacuum into an alternative one, which leads to the breaking of the C and T symmetries. The CPT is the real structure operator; it preserves the normal vacuum. We have proven that, in the theory of the Dirac Sea, the formula for the charge conjugation operator must contain an additional generalized Dirac conjugation operator.

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 Dispersion formulas in QFTs, CFTs and holography

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
David Meltzer
Keyword(s):  
Fourier Transform ◽  
Correlation Functions ◽  
Momentum Space ◽  
Conformal Blocks ◽  
Dispersion Formula ◽  
Space Dispersion

Abstract We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At n-points, the QFT dispersion formula depends on a sum of nested advanced commutators. For CFT four-point functions, we show that the momentum space dispersion formula is equivalent to the CFT dispersion formula, up to possible semi-local terms. We also show that the Polyakov-Regge expansions associated to the momentum space and CFT dispersion formulas are related by a Fourier transform. In the process, we prove that the momentum space conformal blocks of the causal double-commutator are equal to cut Witten diagrams. Finally, by combining the momentum space dispersion formulas with the AdS Cutkosky rules, we find a complete, bulk unitarity method for AdS/CFT correlators in momentum space.

scholarly journals Celestial superamplitude in $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Hongliang Jiang
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Scattering Amplitudes ◽  
Momentum Space ◽  
Ward Identity ◽  
Yang Mills ◽  
Conformal Field ◽  
New Perspective ◽  
Celestial Sphere

Abstract Celestial amplitude is a new reformulation of momentum space scattering amplitudes and offers a promising way for flat holography. In this paper, we study the celestial amplitudes in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of $$ \mathcal{N} $$ N = 4 SYM theory. We also compute the three-point and four-point celestial super-amplitudes explicitly. They can be identified as the conformal correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied $$ \mathcal{N} $$ N = 4 SYM amplitudes via 2D celestial conformal field theory.

scholarly journals Scaling of anisotropic flow and momentum-space densities for light particles in intermediate energy heavy ion collisions

2006 ◽  
Vol 638 (1) ◽  
pp. 50-54 ◽  
Author(s):  
T.Z. Yan ◽  
Y.G. Ma ◽  
X.Z. Cai ◽  
J.G. Chen ◽  
D.Q. Fang ◽  
...  
Keyword(s):  
Momentum Space ◽  
Heavy Ion Collisions ◽  
Heavy Ion ◽  
Intermediate Energy ◽  
Anisotropic Flow ◽  
Ion Collisions ◽  
Light Particles
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