Scalar-Fermion Analytic Bootstrap in 4D

TL;DR

This paper develops an analytic bootstrap method for spinning 4D conformal blocks, analyzing scalar-fermion correlators to identify operator towers and compute their properties, revealing connections to free theories and minimal twist operators.

Contribution

It introduces an analytic bootstrap approach for spinning 4D conformal blocks and computes twists and OPE coefficients for scalar-fermion correlators at leading and sub-leading orders.

Findings

Identifies two infinite towers of fermionic large spin primary operators.

Determines that leading order corresponds to scalar-fermion generalized free theory.

Shows sub-leading order governed by minimal twist bosonic and fermionic operators.

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 $\langle\phi\psi\phi\bar\psi\rangle$. We find that to every pair of primary scalar $\phi$ and fermion $\psi$ 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.