Maximally Helicity Violating Disk Amplitudes, Twistors and Transcendental Integrals

We obtain simple expressions for tree-level maximally helicity violating amplitudes of N gauge bosons from disk world-sheets of open superstrings. The amplitudes are written in terms of (N-3)! hypergeometric integrals depending on kinematic parameters, weighted by certain kinematic factors. The integrals are transcendental in a strict sense defined in this work. The respective kinematic factors can be succinctly written in terms of "dual" momentum twistors. The amplitudes are computed by using the prescription proposed by Berkovits and Maldacena.Comment: 7 page

1/4 BPS States and Non-Perturbative Couplings in N=4 String Theories

We compute certain 2K+4-point, one-loop couplings in the type IIA string compactified on K3 x T^2, which are related to a topological index on this manifold. Their special feature is that they are sensitive to only short and intermediate BPS multiplets. The couplings derive from underlying prepotentials G[K](T,U), which can be nicely summed up into a fundamental generating function. In the dual heterotic string on T^6, the amplitudes describe non-perturbative gravitational corrections to K-loop amplitudes due to bound states of fivebrane instantons with heterotic world-sheet instantons. We argue, as a consequence, that our results also give information about instanton configurations in six dimensional Sp(2k) gauge theories on T^6.Comment: 32 p, harvmac, 1 fig. Revision: taking the fermionic contractions into account, the K3 elliptic genus disappear

Self-Dual Strings and Stability of BPS States in N=2 SU(2) Gauge Theories

We show how BPS states of supersymmetric SU(2) Yang-Mills with matter -both massless and massive- are described as self-dual strings on a Riemann surface. This connection enables us to prove the stability and the strong coupling behaviour of these states. The Riemann surface naturally arises from type-IIB Calabi-Yau compactifications whose three-branes wrapped around vanishing two-cycles correspond to one-cycles on this surface.Comment: 27 LaTex with figs., Some changes in W-boson decay discussion, Refs. adde

Higher Loop Spin Field Correlators in Various Dimensions

We compute higher-point superstring correlators involving spin fields in various even space-time dimensions D at tree-level and to arbitrary loop order. This generalizes previous work in D=4 space-time dimensions. The main focus are D=6,8 and D=10 superstring compactifications for which correlation functions with four and more spin fields are computed. More precisely, we present every non-vanishing six-point function. A number of results can even be derived for arbitrary D. A closed formula for the correlators with any number of fermions psi and two spin fields S in D space-time dimensions is given for arbitrary genus. Moreover, in D=6 and for arbitrary genus, we find a general formula for the correlators . The latter serve as basic building blocks to construct higher-point fermionic correlation functions. In D=8 we can profit from the SO(8)-triality to derive further tree-level correlators with a large numbers of spin fields.Comment: 47 pages, 1 figure; v2: typos corrected; submitted to JHE

Prepotential, Mirror Map and F-Theory on K3

We compute certain one-loop corrections to F^4 couplings of the heterotic string compactified on T^2, and show that they can be characterized by holomorphic prepotentials. We then discuss how some of these couplings can be obtained in F-theory, or more precisely from 7-brane geometry in type IIB language. We in particular study theories with E_8 x E_8 and SO(8)^4 gauge symmetry, on certain one-dimensional sub-spaces of the moduli space that correspond to constant IIB coupling. For these theories, the relevant geometry can be mapped to Riemann surfaces. Physically, the computations amount to non-trivial tests of the basic F-theory -- heterotic duality in eight dimensions. Mathematically, they mean to associate holomorphic 5-point couplings of the form (del_t)^5 G = sum[ g_l l^5 q^l/(1-q^l) ] to K3 surfaces. This can be seen as a novel manifestation of the mirror map, acting here between open and closed string sectors.Comment: 36 pages, 2 figures (published version

Graviton as a Pair of Collinear Gauge Bosons

We show that the mixed gravitational/gauge superstring amplitudes describing decays of massless closed strings - gravitons or dilatons - into a number of gauge bosons, can be written at the tree (disk) level as linear combinations of pure open string amplitudes in which the graviton (or dilaton) is replaced by a pair of collinear gauge bosons. Each of the constituent gauge bosons carry exactly one half of the original closed string momentum, while their +/- 1 helicities add up to +/- 2 for the graviton or to 0 for the dilaton.Comment: 10 pages, harvmac; v2: references adde