No abstract

We investigate compactifications with duality twists and their relation to orbifolds and compactifications with fluxes. Inequivalent compactifications are classified by conjugacy classes of the U-duality group and result in gauged supergravities in lower dimensions with nontrivial Scherk-Schwarz potentials on the moduli space. For certain twists, this mechanism is equivalent to introducing internal fluxes but is more general and can be used to stabilize some of the moduli. We show that the potential has stable minima with zero energy precisely at the fixed points of the twist group. In string theory, when the twist belongs to the T-duality group, the theory at the minimum has an exact CFT description as an orbifold. We also discuss more general twists by nonperturbative Uduality transformations.

The exact entropy of two-charge supersymmetric black holes in N = 4 string theories is computed to all orders using Wald's formula and the supersymmetric attractor equations with an effective action that includes the relevant higher curvature terms. Classically, these black holes have zero area but the attractor equations are still applicable at the quantum level. The quantum corrected macroscopic entropy agrees precisely with the microscopic counting for an infinite tower of fundamental string states to all orders in an asymptotic expansion.A distinctive feature of superstring theory is that its spectrum often contains an infinite tower of BPS states in a given topological sector. The first example of such a tower of BPS states was noticed in the perturbative spectrum of toroidally compactified superstring theories [1,2]. We will be interested here in the heterotic string compactified on T 4 × T 2 where T 4 is a 4-torus in {6789} directions and T 2 is a 2-torus which we take to be a product of two circles in the {45} directions. Consider now a string state with winding number w along the x 5 direction. In a given winding sector, there is a tower of BPS states each in the right-moving ground state but carrying arbitrary left-moving oscillations subject to the Virasoro constraint N L = 1 − nw, where N L is the left-moving oscillation number and n is the quantized momentum along. Note that N L is positive and hence a BPS state that satisfies this constraint has negative n for positive w for large N L . We will henceforth denote these states by (n, w).The number of such states is summarized conveniently by a partition functionwhere N ≡ w|n| = N L − 1. The factor of 16 comes from the degeneracy of the right-moving supersymmetric ground state. Since N L is the number operator for the 24 left-moving transverse bosons, the partition function can be readily evaluatedwhere ∆(q) is the Jacobi discriminant function with argument q = exp (−β). In terms of the Dedekind eta function η(q), the discriminant is given by ∆(q) = η(q) 24 . The number of states at level N is then given by the inverse Laplace transform(3) * Electronic address: atish@tifr.res.inTo find the asymptotic density at large N , we want to take the high temperature limit or β → 0. It is convenient to use the modular property of the discriminantAs e −4π 2 /β → 0, we can then use the asymptotics ∆(q) ∼ q and evaluate the integralin saddle-point approximation. The saddle point occurs at β = 2π/ √ N and the degeneracy has the characteristic exponential growth d N ∼ exp (4π w|n|). The subleading terms can be computed in an asymptotic expansion.This tower of states has played a crucial role in furthering our understanding of dualities and black hole physics. Heterotic string on T 4 × T 2 is dual to Type-IIA on K 3 × T 2 [3,4]. Initial evidence for this duality came from matching the low-lying BPS states and the supergravity action but a far more stringent test is obtained by matching the entire infinite tower of BPS states. The state (n, w) is dual to w NS5-branes ...

We undertake a systematic analysis of non-geometric backgrounds in string theory by seeking stringy liftings of a class of gauged supergravity theories. In addition to conventional flux compactifications and non-geometric T-folds with T-duality transition functions, we find a new class of non-geometric backgrounds with non-trivial dependence on the dual coordinates that are conjugate to the string winding number. We argue that T-duality acts in our class of theories, including those cases without isometries in which the conventional Buscher rules cannot be applied, and that these generalised T-dualities can take T-folds or flux compactifications on twisted tori to examples of the new non-geometric backgrounds. We show that the new class of non-geometric backgrounds and the generalised T-dualities arise naturally in string field theory, and are readily formulated in terms of a doubled geometry, related to generalised geometry. At special points in moduli space, some of the non-geometric constructions become equivalent to asymmetric orbifolds which are known to provide consistent string backgrounds. We construct the bosonic sector of the corresponding gauged supergravity theories and show that they have a universal form in any dimension, and in particular construct the scalar potential. We apply this to the supersymmetric WZW model, giving the complete non-linear structure for a class of WZW-model deformations.

It is argued that the superstring tension is not renormalized in perturbation theory for vacua which preserve N= 1 spacetime supersymmetry. Some implications of this result for macroscopic superstrings are discussed, as well as some analogies between macroscopic superstrings and solitons in supersymmetric theories.