Higher-Spin Gauge Theories and Bulk Locality

TL;DR

The paper establishes a no-go for constructing consistent Noether interactions among massless higher-spin fields on AdS by gauging global higher-spin symmetries, revealing a non-local obstruction at quartic order within the Fronsdal framework. Using the Noether procedure, the authors separate potential interactions into homogeneous pieces fixed by HS symmetry and particular pieces given by exchange amplitudes, demonstrating that the quartic sector cannot be made local without altering the underlying HS structure. Crossing symmetry and the structure of single-trace versus double-trace exchanges drive the obstruction, with HS towers contributing self-dually under crossing. The result implies that achieving interacting HS theories requires new guiding principles beyond classical local field theory, possibly a topological or stringy bulk description, rather than a straightforward extension of the Fronsdal programme.

Abstract

We present a no-go result on consistent Noether interactions among higher-spin gauge fields on anti-de Sitter space-times. We show that there is a non-local obstruction at the classical level to consistent interacting field theory descriptions of massless higher-spin particles that are described in the free limit by the free Fronsdal action, under the assumption that such theories arise from the gauging of a global higher-spin symmetry. Our result suggests that the Fronsdal programme for introducing interactions among higher-spin gauge fields cannot be completed without introducing new guiding principles, which could lie beyond the framework of classical field theory.