Topological amplitudes in heterotic strings with Wilson lines

Abstract

We consider d=4, N = 2 compactifications of heterotic strings with an arbitrary number of Wilson lines. In particular, we focus on known chains of candidate heterotic/type II duals. We give closed expressions for the topological amplitudes F (g) in terms of automorphic forms of SO(2 + k, 2, Z), and find agreement with the geometric data of the dual K3 fibrations wherever those are known.a marlene.weiss@cern.ch

Enhanced gauge groups inN=4topological amplitudes and Lorentzian Borcherds algebras

“…Upon splitting T 6 = T 4 × T 2 , we evaluate F analy 1 explicitly in the large volume limit of T 4 using the method of orbits [10,3] (or in mathematical parlance, the Rankin-Selberg method), for any choice of the unbroken gauge group h ⊂ e 8 ⊕ e 8 . In particular, we allow for h to be semisimple, thus extending previous results in the literature where always one e 8 -factor remained unbroken [3,11,12,13,14,15]. Equivalently, we allow for Wilson lines to be embedded in any of the factors in the sum e 8 ⊕e 8 .…”

“…We will then proceed to study a list of further examples to show that our approach works in great generality. For many of these examples the decomposition of the full Γ 2,18 Siegel-Narain theta-function for non-trivial V has already been considered previously in the literature using the so called 'sequential Higgs mechanism' [43,13]. Our method, however, is more flexible and allows a quick adaptation also for more general cases.…”

Jacobi forms of higher index and paramodular groups in $ \mathcal{N} $ = 2, D = 4 compactifications of string theory

“…We can also compute the Jacobi form φ −2,Λ for these two cases using the orbifold limit. This orbifold computation was essentially done in [29]. By taking Λ = α 1 , α 2 and Λ = α 1 , α 2 , α 3 in our example we match the expressions given above up to order q 2 .…”

“…The prepotential and gravitational coupling are given in terms of the topological properties of the Calabi-Yau (CY) manifold and hence one can study the duality by comparing the results on heterotic side with this topological data as was done in [45,4,29,28,46] for models with Wilson lines. To be more concrete, let us give some definitions.…”

“…Intersection numbers for P 4 (1, 1, 2, 6, 8) [18], which has Hodge numbers (5,161), is given in [45] matching the result above. Heterotic computation at an orbifold point and moduli mapping is also given in [29], where the map was found by comparison to topological information given in [45].…”