Constantin Bachas

Four-Dimensional Superstrings

We solve completely the constraints of factorization and multiloop modular invariance for closed string theories in which all internal quantum numbers of the string are carried by free periodic and antiperiodic world-sheet fermions. We derive a simple set of necessary and sufficient rules, and illustrate how they can be used to find the spectrum, one-loop amplitudes and low-energy lagrangian of many realistic four-dimensional chiral models. We prove that modular invariance and factorization ensure the presence of a massless graviton and the correct connection between spin and statistics. We also prove that the existence of a massless spin-3/2 state ensures the absence of tachyons and the vanishing of the one-loop cosmological constant.

4d fermionic superstrings with arbitrary twists

We present the rules for systematically constructing all consistent four-dimensional string theories, using free world-sheet fermions which pick up arbitrary phases when parallel transported around the string. These rules are necessary and sufficient for multi-loop modular invariance. They lead to theories with general ZN (GSO-type) projections, whose merits for model-building we discuss. We classify all boundary conditions yielding massless space-time spinors. We show that, in contrast to the case of only real 2d fermions, all possible realizations of world-sheet supersymmetry are now allowed. This opens the way for the construction of a new class of supersymmetric string models.

Pair creation of open strings in an electric field

Abstract We calculate exactly the rate of pair production of open bosonic and supersymmetric strings in a constant electric field. The rate agrees with Schwingers classic result in the weak-field limit, but diverges when the electric field approaches some critical value of the order of the string tension.

An expanding universe in string theory

Abstract We present solutions of the bosonic, heterotic and type II string theories, whose space-time manifold is a linearly expanding homogeneous and isotropic universe. These solutions are obtained by giving a background charge to the time coordinate on the world-sheet. We find the spectrum, demonstrate positivity of the Hilbert space up to the second excited level, and construct modular-invariant partition functions. The central charge of transverse excitations is a free parameter that controls the asymptotic density of states; the critical dimension and gauge group can in particular be made arbitrarily large. We show how to construct dual, factorizable, energy-conserving amplitudes in this background, discuss their interpretation and comment on the initial singularity and flatness problems in the light of our results.

Anti-de-Sitter D-branes

We study D-branes of the SL(2,) WZW model and of its discrete orbifolds. Gluing the currents by group automorphisms leads to three types of D-branes: two-dimensional hyperbolic planes (H2), de Sitter branes (dS2), or anti-de Sitter branes (AdS2). We explain that the dS2 branes are unphysical, because the electric field on their world-volume is supercritical. By combining SL(2,) and SU(2), we exhibit a class of supersymmetric AdS2 × S2 three-brane world-volumes, and consider their possible embeddings in the near-horizon region of stringy black holes. We point out the intriguing difference between the induced and the effective geometries of these D-branes, and speculate on its possible significance.

Heterotic / type I duality and D-brane instantons

Abstract We study heterotic/type I duality in d = 8, 9 uncompactified dimensions. We consider the special (”BPS-saturated”) F 4 and R 4 terms in the effective one-loop heterotic action, which are expected to be non-perturbatively exact. Under the standard duality map these translate to tree-level, perturbative and non-perturbative contributions on the type I side. We check agreement with the one-loop open string calculation, and discuss the higher-order perturbative contributions, which arise because of the mild non-holomorphicities of the heterotic elliptic genus. We put the heterotic world-sheet instanton corrections in a form that can be motivated as arising from a D-brane instanton calculation on the type I side.

Aspects of type I– type II– heterotic triality in four dimensions

We discuss the equivalence between Type I, Type II and Heterotic N = 2 superstring theories in four dimensions. We study the effective field theory of Type I models obtained by orientifold reductions of Type IIB compactifications on K3 × T 2 . We show that the perturbative prepotential is determined by the one-loop corrections to the Planck mass and is associated to an index. As is the case for threshold corrections to gauge couplings, this renormalization is entirely due to N = 2 BPS states that originate from D = 6 massless string modes. We apply our result to the so-called S-T-U model which admits simultaneous Type II and Heterotic descriptions, and show that all three prepotentials agree in the appropriate limits as expected from the superstring triality conjecture.

Threshold effects in open string theory

Abstract We analyze the one-loop effective gauge-field action in Z 2 -orbifold compactifications of type-I theory. We show how, for non-abelian group factors, the threshold effects are ultraviolet finite though given entirely by a six-dimensional field theory expression.

Anomalous creation of branes

In certain circumstances when two branes pass through each other a third brane is produced stretching between them. We explain this phenomenon by the use of chains of dualities and the inflow of charge that is required for the absence of chiral gauge anomalies when pairs of D-branes intersect.

Loop operators and the Kondo problem

We analyse the renormalisation group flow for D-branes in WZW models from the point of view of the boundary states. To this end we consider loop operators that perturb the boundary states away from their ultraviolet fixed points, and show how to regularise and renormalise them consistently with the global symmetries of the problem. We pay particular attention to the chiral operators that only depend on left-moving currents, and which are attractors of the renormalisation group flow. We check (to lowest non-trivial order in the coupling constant) that at their stable infrared fixed points these operators measure quantum monodromies, in agreement with previous semiclassical studies. Our results help clarify the general relationship between boundary transfer matrices and defect lines, which parallels the relation between (non-commutative) fields on (a stack of) D-branes and their push-forwards to the target-space bulk.