Exact Supersymmetric String Solutions in Curved Gravitational Backgrounds

TL;DR

This work constructs a class of exact, stable superstring vacua in curved backgrounds using $N=4$ superconformal world-sheet symmetry. By combining four distinct $\hat{c}=4$ realizations—free-field, semi-wormhole, torus-bell, and cigar/trumpet-bell—the authors build modular-invariant spectra and derive explicit partition functions, ensuring spacetime supersymmetry via $N=4$ spectral flow while reducing supersymmetry by a factor of 2 through targeted projections. The constructions connect to four-dimensional gauged supergravities in the weak-curvature limit and to non-critical string theories with a Liouville sector carrying background charges, spanning central charges ${\hat{c}}_M$ in $[5,9]$; special cases reveal massless twisted states. This framework yields exact vacua that illuminate string dynamics in non-trivial geometries, offer a handle on strong-coupling regimes, and provide a modular, unitary foundation for exploring quantum gravity in curved spacetimes.

Abstract

We construct a new class of exact and stable superstring solutions based on $N=4$ superconformal world-sheet symmetry. In a subclass of these, the full spectrum of string excitations is derived in a modular-invariant way. In the weak curvature limit, our solutions describe a target space with non-trivial metric and topology, and generalize the previously known (semi) wormhole. The effective field theory limit is identified in certain cases, with solutions of the $N=4$ and $N=8$ extended gauged supergravities, in which the number of space-time supersymmetries is reduced by a factor of 2 because of the presence of non-trivial dilaton, gravitational and/or gauge backgrounds. In the context of string theory, our solutions correspond to stable non-critical superstrings in the strong coupling region; the super-Liouville field couples to a unitary matter system with central charge $5\le{\hat c}_M\le 9$.