Counting BPS States on the Enriques Calabi-Yau

Abstract

We study topological string amplitudes for the FHSV model using various techniques. This model has a type II realization involving a Calabi-Yau threefold with Enriques fibres, which we call the Enriques Calabi-Yau. By applying heterotic/type IIA duality, we compute the topological amplitudes in the fibre to all genera. It turns out that there are two different ways to do the computation that lead to topological couplings with different BPS content. One of them gives the standard D0-D2 counting amplitudes, and from the other one we obtain information about bound states of D0-D4-D2 branes on the Enriques fibre. We also study the model using mirror symmetry and the holomorphic anomaly equations. We verify in this way the heterotic results for the D0-D2 generating functional for low genera and find closed expressions for the topological amplitudes on the total space in terms of modular forms, and up to genus three. This model turns out to be much simpler than the generic B-model and might be exactly solvable.

Enhanced supersymmetry from vanishing Euler number

“…It is self-mirror and thereby does not have experience any worldsheet instanton corrections at the twoderivative level [33]. There is however a non-trivial pattern of higher-derivative corrections for this background (graviphoton-curvature couplings), some of which have been computed in [35,36]. We begin by considering the harmonic forms on the Enriques Calabi-Yau Y = (K3 × T 2 )/Z τ 2 .…”

Topological amplitudes in heterotic strings with Wilson lines

“…On the heterotic side, these amplitudes appear at 1-loop [3] and are therefore in general accessible to computation [4,5,6,7]. The result can be mapped to the type II side, yielding striking predictions in enumerative geometry.…”

Resolved toroidal orbifolds and their orientifolds

“…They are related to the Schoen CalabiYau manifold [26] (see also [27]) with h 1,1 = h 2,1 = 19, and to the Enriques Calabi-Yau manifold [28], [29] with h 1,1 = h 2,1 = 11.…”