Conformal 3-Point Functions and the Lorentzian OPE in Momentum Space

Marc Gillioz

2020Communications in Mathematical Physics41 citationsDOI Open Access PDF

Abstract

Abstract In conformal field theory in Minkowski momentum space, the 3-point correlation functions of local operators are completely fixed by symmetry. Using Ward identities together with the existence of a Lorentzian operator product expansion (OPE), we show that the Wightman function of three scalar operators is a double hypergeometric series of the Appell $$F_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> type. We extend this simple closed-form expression to the case of two scalar operators and one traceless symmetric tensor with arbitrary spin. Time-ordered and partially-time-ordered products are constructed in a similar fashion and their relation with the Wightman function is discussed.

Topics & Concepts

Operator product expansionMinkowski spaceMathematical physicsScalar (mathematics)Conformal field theoryConformal mapHypergeometric functionPhysicsMathematicsScalar fieldMomentum operatorPosition and momentum spaceOperator (biology)Tensor fieldTensor productConformal symmetryProduct (mathematics)Quantum field theoryScalar field theorySymmetric tensorPure mathematicsFunction (biology)Space (punctuation)Simple (philosophy)Mathematical analysisGeneralized hypergeometric functionFeynman integralLadder operatorMomentum (technical analysis)Series (stratigraphy)Analytic continuationField (mathematics)Correlation function (quantum field theory)Semiclassical physicsQuantum mechanicsPropagatorNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical PhysicsAlgebraic and Geometric Analysis