Chiral $$\Lambda $$-$$\mathfrak {bms}_4$$ symmetry of 3d conformal gravity

Abstract We propose mixed boundary conditions for 3d conformal gravity consistent with variational principle in its second-order formalism that admit the chiral $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> - $$\mathfrak {bms}_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>bms</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> algebra as their asymptotic symmetry algebra. This algebra is one of the four chiral $$\mathcal W$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>W</mml:mi> </mml:math> -algebra extensions of $$\mathfrak {so}(2,3)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>so</mml:mi> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and is a generalisation of the chiral $$\mathfrak {bms}_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>bms</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> algebra responsible for soft theorems of graviton MHV amplitudes in $${\mathbb R}^{1,3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> gravity to the case of non-zero negative cosmological constant. The corresponding charges are shown to be finite and integrable, and realise this non-linear $${{\mathcal {W}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>W</mml:mi> </mml:math> -algebra.