# Scalar-fermion analytic bootstrap in 4D

Elkhidir, Emtinan (0000 0004 1762 9868, grid.5970.b, SISSA, Via Bonomea 265, I-34136, Trieste, Italy) (0000 0004 1936 9457, grid.8993.b, Department of Physics and Astronomy, Uppsala University, SE-751 08, Uppsala, Sweden) ; Karateev, Denis (0000 0004 1762 9868, grid.5970.b, SISSA, Via Bonomea 265, I-34136, Trieste, Italy) (0000000121839049, grid.5333.6, Institute of Physics, EPFL, CH-1015, Lausanne, Switzerland)

12 June 2019

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 ϕ ψ ϕ ψ ¯ $\left\langle \phi\ \psi\ \phi\ \overline{\psi}\right\rangle$ . 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.

Published in: JHEP 1906 (2019) 026 DOI: 10.1007/JHEP06(2019)026
arXiv: 1712.01554