Partially celestial states and their scattering amplitudes

We study representations of the Poincaré group that have a privileged transformation law along a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>p</a:mi></a:math>-dimensional hyperplane, and uncover their associated spinor-helicity variables in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>D</c:mi></c:math> spacetime dimensions. Our novel representations generalize the recently introduced celestial states and transform as conformal primaries of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>S</e:mi><e:mi>O</e:mi><e:mo stretchy="false">(</e:mo><e:mi>p</e:mi><e:mo>,</e:mo><e:mn>1</e:mn><e:mo stretchy="false">)</e:mo></e:math>, the symmetry group of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>p</i:mi></i:math>-hyperplane. We will refer to our generalized states as “partially celestial.” Following Wigner’s method, we find the induced representations, including spin degrees of freedom. Defining generalized spinor-helicity variables for every <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>D</k:mi></k:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>p</m:mi></m:math>, we are able to construct the little group covariant part of partially celestial amplitudes. Finally, we briefly examine the application of the pairwise little group to partially celestial states with mutually nonlocal charges.