W(0,b) algebra and the dual theory of 3D asymptotically flat higher spin gravity

Bondi-Metzner-Sachs (BMS) algebra in three spacetime dimensions can be deformed into a two parameter family of algebra known as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>W</a:mi><a:mo stretchy="false">(</a:mo><a:mi>a</a:mi><a:mo>,</a:mo><a:mi>b</a:mi><a:mo stretchy="false">)</a:mo></a:math> algebra. For <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>a</e:mi><e:mo>=</e:mo><e:mn>0</e:mn></e:math>, we show that other than <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>W</g:mi><g:mo stretchy="false">(</g:mo><g:mn>0</g:mn><g:mo>,</g:mo><g:mo>−</g:mo><g:mn>1</g:mn><g:mo stretchy="false">)</g:mo></g:math>, no other <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>W</k:mi><k:mo stretchy="false">(</k:mo><k:mn>0</k:mn><k:mo>,</k:mo><k:mi>b</k:mi><k:mo stretchy="false">)</k:mo></k:math> algebra admits a nondegenerate bilinear and thus one cannot have a Chern-Simons gauge theory formulation with them. However, they may appear in a three-dimensional gravity description, where we also need to have a spin 2 generator, that comes from the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mo stretchy="false">(</o:mo><o:mi>a</o:mi><o:mo>=</o:mo><o:mn>0</o:mn><o:mo>,</o:mo><o:mi>b</o:mi><o:mo>=</o:mo><o:mo>−</o:mo><o:mn>1</o:mn><o:mo stretchy="false">)</o:mo></o:math> sector. In the present work, we have demonstrated that the asymptotic symmetry algebra of a spin-3 gravity theory on flat spacetime has both the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>W</s:mi><s:mo stretchy="false">(</s:mo><s:mn>0</s:mn><s:mo>,</s:mo><s:mo>−</s:mo><s:mn>1</s:mn><s:mo stretchy="false">)</s:mo></s:math> and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>W</w:mi><w:mo stretchy="false">(</w:mo><w:mn>0</w:mn><w:mo>,</w:mo><w:mo>−</w:mo><w:mn>2</w:mn><w:mo stretchy="false">)</w:mo></w:math> algebras as subalgebras. We have also constructed a dual boundary field theory for this higher spin gravity theory by using the Chern-Simons/Wess-Zumino-Witten correspondence. Published by the American Physical Society 2024