Asymptotic symmetry algebra of N=8 supergravity

The asymptotic symmetry algebra of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">N</a:mi><a:mo>=</a:mo><a:mn>1</a:mn></a:math> supergravity was recently constructed using the well-known two-dimensional celestial conformal field (CFT) theory technique [A. Fotopoulos , ]. In this paper, we extend the construction to the maximally supersymmetric four-dimensional <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi mathvariant="script">N</d:mi><d:mo>=</d:mo><d:mn>8</d:mn></d:math> supergravity theory in asymptotically flat spacetime and construct the extended asymptotic symmetry algebra, which we call <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi mathvariant="script">N</g:mi><g:mo>=</g:mo><g:mn>8</g:mn><g:mtext> </g:mtext><g:mtext> </g:mtext><g:msub><g:mrow><g:mi mathvariant="fraktur">s</g:mi><g:mi mathvariant="fraktur">b</g:mi><g:mi mathvariant="fraktur">m</g:mi><g:mi mathvariant="fraktur">s</g:mi></g:mrow><g:mn>4</g:mn></g:msub></g:math>. We use the celestial CFT technique to find the appropriate currents for extensions of <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi mathvariant="script">N</n:mi><n:mo>=</n:mo><n:mn>8</n:mn></n:math> super-Poincaré and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>SU</q:mi><q:mo stretchy="false">(</q:mo><q:mn>8</q:mn><q:msub><q:mo stretchy="false">)</q:mo><q:mi>R</q:mi></q:msub></q:math> R-symmetry current algebra on the celestial sphere <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msup><u:mrow><u:mi mathvariant="script">C</u:mi><u:mi mathvariant="script">S</u:mi></u:mrow><u:mn>2</u:mn></u:msup></u:math>. We generalize the definition of shadow transformations and show that there is infinite dimensional extension of the global <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>SU</y:mi><y:mo stretchy="false">(</y:mo><y:mn>8</y:mn><y:msub><y:mo stretchy="false">)</y:mo><y:mi>R</y:mi></y:msub></y:math> algebra in the theory. Published by the American Physical Society 2024