Abstract
In this work, building up on [1] we present momentum space Ward identities related to broken higher spin symmetry as an alternate approach to computing correlators of spinning operators in interacting theories such as the quasi-fermionic and quasi-bosonic theories. The direct Feynman diagram approach to computing correlation functions is intricate and in general has been performed only in specific kinematic regimes. We use higher spin equations to obtain the parity even and parity odd contributions to two-, three- and four-point correlators involving spinning and scalar operators in a general kinematic regime, and match our results with existing results in the literature for cases where they are available.One of the interesting facts about higher spin equations is that one can use them away from the conformal fixed point. We illustrate this by considering mass deformed free boson theory and solving for two-point functions of spinning operators using higher spin equations.
Highlights
Conformal Field Theory (CFT) is one of the cornerstones of theoretical physics
In this work, building up on [1] we present momentum space Ward identities related to broken higher spin symmetry as an alternate approach to computing correlators of spinning operators in interacting theories such as the quasi-fermionic and quasi-bosonic theories
The authors showed that three-point correlators in an interacting theory with broken higher spin symmetry can be fixed in terms of three-point functions of the free fermion theory, free boson theory and a parity odd part and they fixed the coefficients of these terms
Summary
Conformal Field Theory (CFT) is one of the cornerstones of theoretical physics. Among other things, it plays an important role in the well celebrated gauge-gravity correspondence, in explaining critical phenomena at phase transitions, and in defining quantum field theories as deformations of theories with conformal symmetry. See the very recent work [39] in which we computed parity odd correlators by solving momentum space conformal Ward identities and using weight-shifting and spin-raising operators. Parity odd correlators are important as they arise in the study of the free fermion theory and theories with slightly broken higher spin symmetry. In appendix F we give some details involved in the computation of correlators in the free massive bosonic theory
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