w1+∞ Algebra with a Cosmological Constant and the Celestial Sphere

It is shown that there exists a simple deformed version of Strominger’s infinite-dimensional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>w</a:mi></a:mrow><a:mrow><a:mn>1</a:mn><a:mo>+</a:mo><a:mi>∞</a:mi></a:mrow></a:msub></a:mrow></a:math> algebra of soft graviton symmetries, which we conjecture to arise in spacetimes with a nonvanishing cosmological constant. The deformed algebra contains a subalgebra generating <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>S</c:mi><c:mi>O</c:mi><c:mo stretchy="false">(</c:mo><c:mn>1</c:mn><c:mo>,</c:mo><c:mn>4</c:mn><c:mo stretchy="false">)</c:mo></c:math> or <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>S</g:mi><g:mi>O</g:mi><g:mo stretchy="false">(</g:mo><g:mn>2</g:mn><g:mo>,</g:mo><g:mn>3</g:mn><g:mo stretchy="false">)</g:mo></g:math> symmetry groups of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>dS</k:mi><k:mn>4</k:mn></k:msub></k:math> or <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>AdS</m:mi><m:mn>4</m:mn></m:msub></m:math>, depending on the sign of the cosmological constant. The transformation properties of soft gauge symmetry currents under the deformed <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi mathvariant="normal">w</o:mi><o:mrow><o:mn>1</o:mn><o:mo>+</o:mo><o:mi>∞</o:mi></o:mrow></o:msub></o:math> are also discussed. Published by the American Physical Society 2024