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Register a new userSpin 2 fluctuations in 1/4 BPS AdS$_3$/CFT$_2$
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Authors
Stefano Speziali
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In this paper we study spin 2 fluctuations around a warped $AdS_3 times S^2 times T^4 times mathcal{I}_{rho}$ background in type IIA supergravity with small $mathcal{N} = (0,4)$ supersymmetry. We find a class of fluctuations, which will be called textit{universal}, that is independent of the background data and corresponds to operators with scaling dimension $Delta = 2l +2$, being $l$ the angular-momentum-quantum-number on the $S^2$ which realises the $SU(2)_R$ symmetry. We compute the central charge for $mathcal{N} = (0,4)$ two-dimensional superconformal theories from the action of the spin 2 fluctuations.
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We study a class of exact supersymmetric solutions of type IIB Supergravity. They have an SO(4) x SU(2) x U(1) isometry and preserve generically 4 of the 32 supersymmetries of the theory. Asymptotically AdS_5 x S^5 solutions in this class are dual to 1/8 BPS chiral operators which preserve the same symmetries in the N=4 SYM theory. We analyse the solutions to these equations in a large radius asymptotic expansion: they carry charges with respect to two U(1) KK gauge fields and their mass saturates the expected BPS bound. We also show how the same formalism is suitable for the description of the AdS_5 x Y^{p,q} geometries and a class of their excitations.
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The Ryu-Takayanagi conjecture contradicts $1+1$-dimensional CFT if we apply it to two far disjoint intervals because it predicts the product state. Instead of the conventional conjecture, we propose a holographic entanglement entropy formula that the entanglement entropy of two disjoint intervals is described by the appropriate sum of the area of signed extremal curves. We confirm that the resulting holographic entanglement entropy is consistent with the entanglement entropy for the specific two disjoint intervals evaluated in the large $c$ limit CFT.
We study the strong coupling behaviour of $1/4$-BPS circular Wilson loops (a family of latitudes) in ${cal N}=4$ Super Yang-Mills theory, computing the one-loop corrections to the relevant classical string solutions in AdS$_5times$S$^5$. Supersymmetric localization provides an exact result that, in the large t Hooft coupling limit, should be reproduced by the sigma-model approach. To avoid ambiguities due to the absolute normalization of the string partition function, we compare the $ratio$ between the generic latitude and the maximal 1/2-BPS circle: Any measure-related ambiguity should simply cancel in this way. We use Gelfand-Yaglom method to calculate the relevant functional determinants, that present some complications with respect to the standard circular case. After a careful numerical evaluation of our final expression we still find disagreement with the localization answer: The difference is encoded into a precise remainder function. We comment on the possible origin and resolution of this discordance.
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