Spacetime supersymmetry in $AdS_3$ backgrounds

TL;DR

Addresses how to realize $N=2$ spacetime supersymmetry in string backgrounds with $AdS_3$ factors by starting from a worldsheet $N=2$ SCFT and engineering $X$ as a circle bundle over a product of Kazama–Suzuki cosets. The authors identify a decomposition $AdS_3\times X \simeq \left( SL(2)/U(1)\right)\times\left( X/U(1)\right)\times U(1)^2$ and modify the worldsheet $U(1)_R$ current to $J_R'$ to recover the correct spacetime algebra, obtaining a consistent $N=2$ spacetime superconformal structure with $c_{st}=kp$ and a spectrum amenable to free-field computations. They analyze target-space consistency constraints, discuss specific geometries such as $AdS_3\times S^3\times T^4$ and $AdS_3\times S^3\times S^3\times U(1)$, and develop vertex-operator constructions in the free-field regime, including GSO projections and mass-shell conditions. The work provides exact CFT tools to probe full string spectra and spacetime CFT data beyond supergravity, with implications for $1/N$ corrections and modular-invariant partition functions, while noting technical challenges from screenings and non-compact cosets.

Abstract

We construct string target spacetimes with AdS_3 x X geometry, which have an N=2 spacetime superconformal algebra. X is found to be a U(1) fibration over a manifold which is a target for an N=2 worldsheet conformal field theory. We emphasize theories with free field realizations where in principle it is possible to compute the full one-particle string spectrum.