Fivebrane instantons and higher derivative couplings in type I theory

We express the infinite sum of D-fivebrane instanton corrections to ${\cal R}^2$ couplings in ${\cal N}=4$ type I string vacua, in terms of an elliptic index counting 1/2-BPS excitations in the effective $Sp(N)$ brane theory. We compute the index explicitly in the infrared, where the effective theory is argued to flow to an orbifold CFT. The form of the instanton sum agrees completely with the predicted formula from a dual one-loop computation in type IIA theory on $K3\times T^2$. The proposed CFT provides a proper description of the whole spectrum of masses, charges and multiplicities for 1/2- and 1/4- BPS states, associated to bound states of D5-branes and KK momenta. These results are applied to show how fivebrane instanton sums, entering higher derivative couplings which are sensitive to 1/4-BPS contributions, also match the perturbative results in the dual type IIA theory.Comment: 14 pages, corrected some typos. Version to appear in Nucl. Phys.

One Loop Partition Function in Plane Waves R-R Background

We compute the one loop partition function of type IIB string in plane wave R-R 5-form background $F^5$ using both path integral and operator formalisms and show that the two results agree perfectly. The result turns out to be equal to the partition function in the flat background. We also study the Tadpole cancellation for the unoriented closed and open string model in plane wave R-R 5-form background studied in hep-th/0203249 and find that the cancellation of the Tadpole requires the gauge group to be SO(8).Comment: 12 pages, no figures, latex, misprint corrected and reference added; to appear in JHE

Generalized Continuity Equation for Quasi-Hermitian Hamiltonians

The continuity relation is generalized to quasi-Hermitian one-dimensional Hamiltonians. As an application we show that the reflection and transmission coefficients computed with the generalized current obey the conventional unitarity relation for the continuous double delta function potential