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

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

Periods, Coupling Constants and Modular Functions in N=2 SU(2) SYM with Massive Matter

We determine the mass dependence of the coupling constant for N=2 SYM with N_f=1,2,3 and 4 flavours. All these cases can be unified in one analytic expression, given by a Schwarzian triangle function. Moreover we work out the connection to modular functions which enables us to give explicit formulas for the periods. Using the form of the J-functions we are able to determine in an elegant way the couplings and monodromies at the superconformal points.Comment: Some changes, final version to appear in IJMPA. 14 LaTex page

Flux-induced Soft Supersymmetry Breaking in Chiral Type IIB Orientifolds with D3/D7-Branes

We discuss supersymmetry breaking via 3-form fluxes in chiral supersymmetric type IIB orientifold vacua with D3- and D7-branes. After a general discussion of possible choices of fluxes allowing for stabilizing of a part of the moduli, we determine the resulting effective action including all soft supersymmetry breaking terms. We also extend the computation of our previous work concerning the matter field metrics arising from various open string sectors, in particular focusing on the 1/2 BPS D3/D7-brane configuration. Afterwards, the F-theory lift of our constructions is investigated.Comment: 55 pages, harvma