String Islands

We discuss string theories with small numbers of non-compact moduli and describe constructions of string theories whose low-energy limit is described by various pure supergravity theories. We also construct a D=4,N=4 compactification of type II string theory with 34 vector fields.Comment: An erroneous example removed. We thank Massimo Bianchi and Cumrun Vafa for pointing out this erro

Moonshine in Fivebrane Spacetimes

We consider type II superstring theory on $K3 \times S^1 \times \mathbb{R}^{1,4}$ and study perturbative BPS states in the near-horizon background of two Neveu-Schwarz fivebranes whose world-volume wraps the $K3 \times S^1$ factor. These states are counted by the spacetime helicity supertrace $\chi_2(\tau)$ which we evaluate. We find a simple expression for $\chi_2(\tau)$ in terms of the completion of the mock modular form $H^{(2)}(\tau)$ that has appeared recently in studies of the decomposition of the elliptic genus of K3 surfaces into characters of the N=4 superconformal algebra and which manifests a moonshine connection to the Mathieu group $M_{24}$.Comment: 32 page

An Uplifting Discussion of T-Duality

It is well known that string theory has a T-duality symmetry relating circle compactifications of large and small radius. This symmetry plays a foundational role in string theory. We note here that while T-duality is order two acting on the moduli space of compactifications, it is order four in its action on the conformal field theory state space. More generally, involutions in the Weyl group $W(G)$ which act at points of enhanced $G$ symmetry have canonical lifts to order four elements of $G$, a phenomenon first investigated by J. Tits in the mathematical literature on Lie groups and generalized here to conformal field theory. This simple fact has a number of interesting consequences. One consequence is a reevaluation of a mod two condition appearing in asymmetric orbifold constructions. We also briefly discuss the implications for the idea that T-duality and its generalizations should be thought of as discrete gauge symmetries in spacetime.Comment: 47 pages, claims regarding $Z_4$ valued cocycles remove