Abstract
We showed that there is no SU(2) Witten anomaly in a large class of 4d mathcal{N} = 2 supersymmetric Heterotic string compactifications. The consistency conditions we consider are the modularity of the new supersymmetric index, the integrality of BPS indices, and the discrete Peccei-Quinn shift symmetries. We also found an example where these conditions are not sufficient to show that the theory is anomaly free. This suggests that there are more conditions in the worldsheet SCFT essential for consistent string compactifications.
Highlights
Lattice W and the charge vector v0 stays within W ∨
We showed that there is no SU(2) Witten anomaly in a large class of 4d N = 2 supersymmetric Heterotic string compactifications
We show that the SU(2) Witten anomaly vanishes if ΛS has a decomposition ΛS = U ⊕ W and v0 ∈ W ∨ ⊂ Λ∨S; here, the lattice W is even and negative definite and is assumed to have a primitive embedding into U ⊕2 ⊕ E8[−1]⊕2
Summary
In the dual Type IIA language, dabc’s are the intersection numbers of the internal Calabi-Yau threefold. Since 2qv is integral and (2qv)3 ≡ 2qv mod 2, this condition is nothing but the condition (2.3) which means the theory is free from Witten anomaly; only neutral states under U(1)’s contribute to (4.5) as stated earlier, which are states corresponding to v’s that are parallel to v0. They are massless when the SU(2) is enhanced
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