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Résumé |
In this talk I will consider type IIB string theory on $AdS_5\times S^5/\mathbb{Z}_L$ orbifold spaces with arbitrary L. Recent localisation results in the dual 4d $N=2$ circular quiver gauge theories provide us with strong coupling expansions of certain correlators involving twisted half-BPS operators. To leading order, these results have been matched to an effective theory for massless twisted string states, constructed by resolving the orbifold singularity and considering localised supergravity modes on the resolution cycles. Applying this reasoning to subleading order in strong coupling, we observe that for $L\neq 2,3,4,6$, a naive reduction of the 10d $(\alpha^\prime)^3$-correction does not result in the correct coefficients to match the localisation result. This mismatch may be explained by the appearance of twisted sector resonances in string amplitudes involving external twisted sector states. Indeed, performing the low-energy expansion of a ?twisted? Virasoro-Shapiro amplitude, one recovers the expected coefficients, suggesting that the orbifold resolution and the low-energy expansion cannot be interchanged directly. If time permits, I will also sketch more recent developments in the understanding of the ?long? quiver limit, arising as $L$ is taken to infinity, from the string theory side. |
