BMS3 fermionic localization

A bstract We consider the geometric action formulation for 3d pure gravity with vanishing cosmological constant. We use fermionic localization to compute the exact torus partition function for a constant representative coadjoint orbit of $$ {\hat{\textrm{BMS}}}_3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>BMS</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> <mml:mn>3</mml:mn> </mml:msub> </mml:math> . This allows us to discuss its 1-loop exactness.