Renormalised CFT 3-point functions of scalars, currents and stress tensors

Understand

We discuss the renormalisation of mixed 3-point functions involving tensorial and scalar operators in conformal field theories of general dimension.

• In previous work we analysed correlators of either purely scalar or purely tensorial operators, in each case finding new features and new complications: for scalar correlators, renormalisation leads to beta functions, novel conformal anomalies of type B, and unexpected analytic structure in momentum space; for correlators of stress tensors and/or conserved currents, beta functions vanish but anomalies of both type B and type A (associated with a $0/0$ structure) are present.
• Mixed correlators combine all these features: beta functions and anomalies of type B, plus the possibility of new type A anomalies.
• Following a non-perturbative and general momentum-space analysis, we present explicit results in dimensions $d=3,4$ for all renormalised 3-point functions of stress tensors, conserved currents and scalars of dimensions $\Delta=d$ and $\Delta=d-2$.