Exploring the twisted sector of ${\mathbb{Z}}_L$ orbifolds: Matching ${\alpha }^{\prime }$-corrections to localisation

Abstract

We consider type IIB string theory on ${\mathrm{AdS}}_5\times S^5/{\mathbb{Z}}_L$ orbifold spaces with generic $L$. Recent localisation results in the dual 4d $\mathcal{N}=2$ 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, which can be 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 $L\ne 2,3,4,6$, a naive reduction of the 10d $({\alpha }^{\prime }{)}^3$-correction does not result in the correct coefficients to match the localisation result. We explain this mismatch by the appearance of twisted sector resonances in string amplitudes involving external twisted sector states. We perform the low-energy expansion of a ``twisted'' Virasoro-Shapiro amplitude and recover the expected coefficients, suggesting that the orbifold resolution and the low-energy expansion can not be interchanged directly. Finally, we comment on the long-quiver limit, $L\to \infty$, in the context of the low-energy effective action.

v2: 38 pages, 4 figures, to be published in JHEP, minor comments added

References in corpus (8)

• The AdS Virasoro-Shapiro Amplitude
• Exact results in a N=2 superconformal gauge theory at strong coupling
• Localization vs holography in $4d$ $\mathcal{N}=2$ quiver theories
• Structure constants in $\mathcal{N}=2$ superconformal quiver theories at strong coupling and holography
• Strong coupling expansions in $\mathcal{N}=2$ quiver gauge theories
• Non-planar corrections in orbifold/orientifold $\mathcal{N}=2$ superconformal theories from localization
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• Integrability treatment of AdS/CFT orbifolds