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Extra info for Communications In Mathematical Physics - Volume 280
The relevant part of the D2 brane moduli space to curves C in the fiber hence localizes to curves which sit in the Enriques fibre. It is therefore sufficient to consider curves in the four special Enriques fibres to explain the BPS numbers in the tables in Sect. 5. Let us first recall an important fact about curves in an Enriques surfaces. 1 in , for every such C in the class r in the Kähler cone there is a second curve C + K E in the class r up to torsion with |C + K E | = ∅ and r 2 = [C]2 = [C + K E ]2 .
23) =1 In this equation, r 2 is computed with the norm of the reduced lattice K , and the restriction r > 0 means that we consider vectors such that Im(r · y) > 0, as well as a finite number of boundary cases [24,43]. 24) where Lin is the polylogarithm of index n defined as ∞ Lin (x) = k=1 xk . 25) In the above expression for Fg we are not taking into account constant terms as well as polynomial terms in y and Im y which also appear in the heterotic computation [24,43]. 2. BPS content of the Fg couplings.
Mariño Table 1. ζ J , α J and β J for the different blocks J ζJ αJ βJ 1 2 δ 0 2 1/2 0 δ 3 1/2 δ δ Let us now consider the fermionic sector in detail. The fermions in the s1,1 lattice do not change under the Z2 symmetry, so together with the fermions in the uncompactified directions we have Z f 1,1 s ϑ = a b 3/2 a b (τ ) η(τ ) . 12) The orbifold blocks for two complex fermions with symmetry ψ → −ψ are given by (see for example , Eq. 13) (τ ) η2 The treatment of the two fermions coming from The 00 block in the a, b sector is simply Z .