D‐instantons and effective couplings in intersecting D‐brane models

This article is basically a rendition of the author's PhD thesis. We are concerned with two aspects of intersecting D6‐brane models: We treat some of the effects that are induced by E2‐instantons and we consider one‐loop corrections to the gauge kinetic functions in the low‐energy effective field theory. Owing to the genesis of this article, we begin in Sect. 1 with a general introduction covering the question why to consider string theory as a candidate theory of nature. After that, in Sect. 2, we go over some topics related to field theory instantons and finally discuss the instanton generated superpotential in supersymmetric QCD (SQCD), the so‐called Affleck–Dine–Seiberg (ADS) superpotential. In Sect. 3 we then proceed to reproduce the ADS superpotential in an intersecting D6‐brane realization of SQCD as the effect of a single E2‐instanton. In order to do so, we first explicate the necessary formalism for calculating the E2‐instanton contribution to the superpotential, then construct a (local) intersecting D6‐brane realization of SQCD, and finally show that the formalism indeed leads to the Affleck–Dine–Seiberg superpotential. In Sect. 4 we consider one‐loop corrections to the gauge kinetic functions. These one‐loop corrections are related quite intricately to gauge threshold corrections which we compute for intersecting D6‐brane models on the ℤ 2 × ℤ 2 toroidal orbifold. An analysis of the formulas for calculating the E2‐instanton contribution to the superpotential raises the question whether this contribution is a holomorphic quantity. In Sect. 5 we take up this question showing that it is indeed holomorphic. In addition, we discuss under which circumstances one can expect E2‐instanton corrections to the gauge kinetic functions.