One-loop determinants in AdS3 supergravity with extended supersymmetry

A bstract We re-examine the computation of the one-loop partition function of Type II supergravity theory compactified on AdS 3 × S 3 × X , where X can be K 3 , T 4 and S 3 × S 1 . These backgrounds preserve eight supercharges (four left and four right moving) and are known to be holographically dual to either small or large $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = (4, 4) superconformal field theories. By extending well-established heat kernel techniques, we evaluate the one-loop determinants associated to these supergravity backgrounds. The resulting expressions are then used to reconstruct the characters of short multiplets of the corresponding dual boundary theories. A distinctive aspect of our analysis is the emergence of contributions from multiple gravitational saddle points in the path integral, reflecting the spectral flow structure present in the boundary theory.