Non-Perturbative Gravitational Corrections in a Class of N=2 String Duals

TL;DR

This paper explores non-perturbative gravitational corrections in specific N=2 string dual pairs, comparing heterotic and type II models, and analyzing instanton effects and supersymmetry breaking.

Contribution

It provides new constructions of dual pairs with specific Hodge numbers and computes perturbative corrections, enhancing understanding of N=2 string dualities and non-perturbative effects.

Findings

Perturbative corrections are computed and matched across dual models.

New dual pairs with specific Hodge numbers are constructed.

Instanton numbers are restricted to multiples of 2 or 4 depending on the model.

Abstract

We investigate the non-perturbative equivalence of some heterotic/type II dual pairs with N=2 supersymmetry. The perturbative heterotic scalar manifolds are respectively SU(1, 1)/U(1) x SO(2, 2+NV)/ SO(2) x SO(2+NV) and SO(4, 4+NH)/ SO(4) x SO(4+NH) for moduli in the vector multiplets and hypermultiplets. The models under consideration correspond, on the type II side, to self-mirror Calabi-Yau threefolds with Hodge numbers h(1,1)= NV +3= h(2,1)= NH +3, which are K3 fibrations. We consider three classes of dual pairs, with NV=NH=8, 4 and 2. The models with h(1,1)=7 and 5 provide new constructions, while the h(1,1)=11, already studied in the literature, is reconsidered here. Perturbative R2-like corrections are computed on the heterotic side by using a universal operator whose amplitude has no singularities in the (T,U) space, and can therefore be compared with the type II side result. We point out several properties connecting K3 fibrations and spontaneous breaking of the N=4 supersymmetry to N=2. As a consequence of the reduced S- and T- duality symmetries, the instanton numbers in these three classes are restricted to integers, which are multiples of 2, 2 and 4, for NV=8, 4 and 2, respectively.