Conformal Field Theory Correlators from Classical Field Theory on Anti-de Sitter Space II. Vector and Spinor Fields

TL;DR

This paper extends the AdS/CFT framework to compute CFT correlators for vector and Dirac fields by carefully implementing a Dirichlet boundary value problem on AdS$_{d+1}$. It derives explicit bulk solutions and on-shell actions to obtain boundary two-point functions with correct conformal dimensions: for vectors, the current $J_i$ has dimension $\tilde{\Delta}=\sqrt{(d-2)^2/4+m^2}$ and a transverse tensor structure, while for Dirac fields, boundary spinors have dimension $m+d/2$ and only half the bulk components are accessible on the boundary. The work also computes the vector–spinor–spinor three-point function and verifies Ward identities without requiring additional boundary terms, strengthening the holographic dictionary for spinor and vector fields and providing new conformal data for CFTs dual to AdS theories. These results illuminate how bulk AdS dynamics encode boundary conformal data and offer tools for exploring more complex correlators in holographic CFTs.

Abstract

We use the AdS/CFT correspondence to calculate CFT correlation functions of vector and spinor fields. The connection between the AdS and boundary fields is properly treated via a Dirichlet boundary value problem.