Entropy of flat space cosmologies from celestial dual

We construct a one-dimensional dual theory that effectively describes the sector of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mo stretchy="false">(</a:mo><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn><a:mo stretchy="false">)</a:mo><a:mi mathvariant="normal">D</a:mi></a:mrow></a:math> flat gravity phase space near a flat space cosmology saddle labeled by definite mass and angular momentum. This Schwarzian-type action describes the dynamics of the (pseudo-)Goldstone bosons of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mrow><f:msub><f:mrow><f:mi>BMS</f:mi></f:mrow><f:mrow><f:mn>3</f:mn></f:mrow></f:msub></f:mrow></f:math> algebra on a circle as the symmetry is spontaneously and anomalously broken. This 1D theory, living on the celestial circle, provides the first explicit construction of a celestial dual theory in <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:mo stretchy="false">(</h:mo><h:mn>2</h:mn><h:mo>+</h:mo><h:mn>1</h:mn><h:mo stretchy="false">)</h:mo><h:mi mathvariant="normal">D</h:mi></h:mrow></h:math>. We use it to calculate the semiclassical entropy of flat space cosmologies and find perfect agreement with existing literature.