One-loop determinants in AdS${}_3$ supergravity with extended supersymmetry

Abstract

We re-examine the computation of the one-loop partition function of Type II supergravity theory compactified on $Ad{S}_3\times {\mathbf{S}}^3\times X$, where $X$ can be $K_3$, $T^4$ and ${\mathbf{S}}^3\times {\mathbf{S}}^1$. These backgrounds preserve eight supercharges (four left and four right moving) and are known to be holographically dual to either small or large $N=(4,4)$ 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.

37 pages