No abstract

We show how turning on Flux for RR (and NS-NS) field strengths on non-compact Calabi-Yau 3-folds can serve as a way to partially break supersymmetry from N = 2 to N = 1 by mass deformation. The freezing of the moduli of Calabi-Yau in the presence of the flux is the familiar phenomenon of freezing of fields in supersymmetric theories upon mass deformations.

We show that certain type II string amplitudes at genus g are given by the topological partition function F g discussed recently by Bershadsky, Cecotti, Ooguri and Vafa.These amplitudes give rise to a term in the four-dimensional effective action of the form g F g W 2g , where W is the chiral superfield of N = 2 supergravitational multiplet. The holomorphic anomaly of F g is related to non-localities of the effective action due to the propagation of massless states. This result generalizes the holomorphic anomaly of the one loop case which is known to lead to non-harmonic gravitational couplings.⋆

We study spontaneous supersymmetry breaking in N = 2 globally supersymmetric theories describing a system of abelian vector multiplets. We find that the most general form of the action admits, in addition to the usual Fayet-Iliopoulos term, a magnetic Fayet-Iliopoulos term for the auxiliary components of dual vector multiplets.In a generic case, N = 2 supersymmetry is broken down spontaneously to N = 1.In some cases however, the scalar potential can drive the theory towards a N = 2 supersymmetric ground state where massless dyons condense in the vacuum.

We test the recently conjectured duality between N =2 supersymmetric type II and heterotic string models by analysing a class of higher dimensional interactions in the respective low-energy Lagrangians. These are F -terms of the form F g W 2g where W is the gravitational superfield. On the type II side these terms are generated at the g-loop level and in fact are given by topological partition functions of the twisted Calabi-Yau sigma model. We show that on the heterotic side these terms arise at the one-loop level. We study in detail a rank 3 example and show that the corresponding couplings F g satisfy the same holomorphic anomaly equations as in the type II case.Moreover we study the leading singularities of F g 's on the heterotic side, near the enhanced symmetry point and show that they are universal poles of order 2g−2 with coefficients that are given by the Euler number of the moduli space of genus-g Riemann surfaces. This confirms a recent conjecture that the physics near conifold singularity is governed by c=1 string theory at the self-dual point.