2020/05/31 by Sachin Jain, Renjan Rajan John, Vinay Malvimat · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Conformal map #Conformal symmetry #Momentum (technical analysis) #Operator (biology) #Operator product expansion #Particle physics theoretical and experimental studies #Position and momentum space #Scalar (mathematics) #Spin (aerodynamics) #Spinning #hep-th
paper · pdf · doi:10.1007/jhep11(2020)049
published as JHEP 11(2020), 049 · Typos fixed, references added, a comment on the scalar five point function in the free fermionic theory removed
openalex created_date 2020/05/21 · arxiv created 2020/07/13 · openalex publication_date 2020/11/01 · arxiv updated 2020/11/18 · openalex updated_date 2026/08/05
A bstract In this article, we explicitly compute in momentum space the three and four-point correlation functions involving scalar and spinning operators in the free bosonic and the free fermionic theory in three dimensions. We also evaluate the five-point function of the scalar operator in the free bosonic theory. We discuss techniques which are more efficient than the usual PV reduction to evaluate one loop integrals. Our techniques can be easily generalised to momentum space correlators of complicated spinning operators and to higher point functions. The three dimensional fermionic theory has the interesting feature that the scalar operator ψψ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>ψ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>ψ</mml:mi> </mml:math> is odd under parity. To account for this, we develop a parity odd basis which is useful to write correlation functions involving spinning operators and an odd number of ψψ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>ψ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>ψ</mml:mi> </mml:math> operators. We further study higher spin (HS) equations in momentum space which are algebraic in nature and hence simpler than their position space counterparts. We use them to solve for three-point functions involving spinning operators without invoking conformal invariance. However, at the level of four-point functions, solving the HS equation requires additional constraints that come from conformal invariance and we could only verify that our explicit results solve the HS equation.