Toward higher-spin symmetry breaking in the bulk

We present a new vacuum of the bosonic higher-spin gauge theory in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>d</a:mi><a:mo>+</a:mo><a:mn>1</a:mn></a:math> dimensions, which has leftover symmetry of the Poincaré algebra in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>d</c:mi></c:math> dimensions. Its structure is very simple: the space-time geometry is that of anti–de Sitter space, while the only nonzero field is a scalar. The scalar extends along the Poincaré radial coordinate <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="normal">z</e:mi></e:math> and is shown to be linearly exact for an arbitrary mixture of its two <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi mathvariant="normal">Δ</h:mi><h:mo>=</h:mo><h:mn>2</h:mn></h:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi mathvariant="normal">Δ</k:mi><k:mo>=</k:mo><k:mi>d</k:mi><k:mo>−</k:mo><k:mn>2</k:mn></k:math> conformal branches. The obtained vacuum breaks the global higher-spin symmetry, leading to a broken phase that lives in the Minkowski space-time.