Scalar Field Corrections to AdS_4 Gravity from Higher Spin Gauge Theory

TL;DR

This work computes the complete ${\mathcal O}(\phi^2)$ stress-energy contributions from a scalar field within the minimal bosonic higher spin theory in AdS$_4$, revealing an infinite tower of higher-derivative terms in the corrected Einstein equation. Using a weak-field expansion in the hs(4) framework, the authors derive a closed-form structure for thequadratic-in-$\phi$ corrections, with the total sign controlled by ${\rm Re}\{b_1^2\}$ and the scalar's parity. The results advance the understanding of graviton-$\phi^2$ couplings and lay groundwork for the cubic action in the spin-0 and spin-2 sector, while highlighting challenges related to energy positivity and boundary conditions. The analysis also points to intriguing connections with holography and potential cosmological applications, motivating further study of domain-wall solutions and bulk/boundary consistency checks.

Abstract

We compute the complete contribution to the stress-energy tensor in the minimal bosonic higher spin theory in D=4 that is quadratic in the scalar field. We find arbitrarily high derivative terms, and that the total sign of the stress-energy tensor depends on the parity of the scalar field.