Finite entanglement entropy in string theory

We analyze the one-loop quantum entanglement entropy in ten-dimensional type-II string theory using the orbifold method by analytically continuing in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>N</a:mi></a:math> the genus-one partition function for string orbifolds on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi mathvariant="double-struck">R</c:mi><c:mn>2</c:mn></c:msup><c:mo>/</c:mo><c:msub><c:mi mathvariant="double-struck">Z</c:mi><c:mi>N</c:mi></c:msub></c:math> conical spaces known for all odd integers <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>N</g:mi><g:mo>></g:mo><g:mn>1</g:mn></g:math>. We show that the tachyonic contributions to the orbifold partition function can be appropriately summed and analytically continued to an expression that is finite in the physical region <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mn>0</i:mn><i:mo><</i:mo><i:mi>N</i:mi><i:mo>≤</i:mo><i:mn>1</i:mn></i:math> resulting in a finite and calculable answer for the entanglement entropy. We discuss the implications of the finiteness of the entanglement entropy for the information paradox, quantum gravity, and holography. Published by the American Physical Society 2024