Scalar-Fermion Analytic Bootstrap in 4D
Emtinan Elkhidir, Denis Karateev
TL;DR
The paper extends analytic bootstrap techniques to spinning 4D CFTs by studying the scalar-fermion four-point function ⟨φ ψ φ \\barψ⟩. It demonstrates that each scalar-fermion pair seeds two infinite towers of large-spin fermionic operators, computes their twists and OPE coefficient products at leading and subleading orders, and shows the leading data matches a scalar-fermion generalized free theory while subleading corrections originate from minimal-twist bosonic and fermionic operators. The authors develop a practical analytic bootstrap recipe, apply it to both s-t and u-t channels, and establish a precise link between the analytic bootstrap results and GFT data, including explicit closed-form expressions in the large-spin limit. The work provides both conceptual insights into spinning correlators and concrete computational tools (Mathematica notebooks) to reproduce and extend the analysis, with implications for AdS interpretations and future spinning inversion approaches.
Abstract
In this work we discuss an analytic bootstrap approach [1,2] in the context of spinning 4D conformal blocks [3,4]. As an example we study the simplest spinning case, the scalar-fermion correlator $\langleφψφ\barψ\rangle$. We find that to every pair of primary scalar $φ$ and fermion $ψ$ correspond two infinite towers of fermionic large spin primary operators. We compute their twists and products of OPE coefficients using both s-t and u-t bootstrap equations to the leading and sub-leading orders. We find that the leading order is represented by the scalar-fermion generalized free theory and the sub-leading order is governed by the minimal twist bosonic (light scalars, currents and the energy-momentum tensor) and fermionic (light fermions and the suppersymmetric current) operators present in the spectrum.