"Reﬁned BPS Invariants of del Pezzo and half K3 Calabi-Yau manifolds"
The most detailed information about rigid N = 2 ﬁve-dimensional supersymmetric theories is contained in a supersymmetric index counting reﬁned BPS states. These states fall into representations of SU(2)L × SU(2)R, the little group in ﬁve dimensions, which has an induced action on the cohomology of the moduli space of stable pairs.
We present the computation of reﬁned BPS state multiplicities associated to M-Theory reductions on local Calabi Yau manifolds, which are based on del Pezzo surfaces and the half K3 using the reﬁned holomorphic anomaly equation and modularity properties.
We conclude by presenting important applications of the obtained results, including E-, M- and [p,q]-Strings.