Holographic Carrollian conformal field theories pseudoentropy

According to the flat/CCFT correspondence, Carrollian conformal field theories (CCFT) in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>d</a:mi> </a:mrow> </a:math> dimensions are dual to asymptotically flat spacetimes in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>d</c:mi> <c:mo>+</c:mo> <c:mn>1</c:mn> </c:math> dimensions. In this paper, starting from the holographic interpretation of pseudoentropy in the (A) <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mtext>dS</e:mtext> <e:mn>3</e:mn> </e:msub> <e:mo>/</e:mo> <e:msub> <e:mrow> <e:mi>CFT</e:mi> </e:mrow> <e:mn>2</e:mn> </e:msub> </e:math> , we show that both extremal spacelike and timelike curves possess a well-defined flat-space limit. The length of these curves can be regarded as the real and imaginary parts of the pseudoentropy for the underlying field theory, where only the real part has been considered thus far. Our calculations can confirm that the entanglement entropy in the CCFTs is fundamentally pseudoentropy.