For generic Z_L orbifolds, naive reduction of the 10d (α')^3 correction fails to match localisation results for twisted half-BPS correlators except at special L values; expanding a twisted Virasoro-Shapiro amplitude recovers the correct coefficients by accounting for twisted sector resonances.
Metric Building of pp Wave Orbifold Geometries
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abstract
We study strings on orbifolds of $AdS_{5}\times S^5$ by SU(2) discrete groups in the Penrose limit. We derive the degenerate metrics of pp wave of $AdS_{5}\times S^5/\Gamma$ using ordinary $ADE$ and affine $\wildtilde{ADE}$ singularities of complex surfaces and results on ${\cal N}=4$ CFT$_4$'s. We also give explicit metric moduli depencies for abelian and non abelian orbifolds.
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Exploring the twisted sector of $\mathbb{Z}_{L}$ orbifolds: Matching $\alpha'$-corrections to localisation
For generic Z_L orbifolds, naive reduction of the 10d (α')^3 correction fails to match localisation results for twisted half-BPS correlators except at special L values; expanding a twisted Virasoro-Shapiro amplitude recovers the correct coefficients by accounting for twisted sector resonances.