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1. Entanglement negativity and replica symmetry breaking in general holographic states

   https://doi.org/10.1007/JHEP01(2025)022  

   Dong, Xi; Kudler-Flam, Jonah; Rath, Pratik (January 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> The entanglement negativity$$ \mathcal{E} $$ $E$(A:B) is a useful measure of quantum entanglement in bipartite mixed states. In random tensor networks (RTNs), which are related to fixed-area states, it was found in ref. [1] that the dominant saddles computing the even Rényi negativity$$ {\mathcal{E}}^{(2k)} $$ $E^{\left(2k\right)}$generically break theℤ_2kreplica symmetry. This calls into question previous calculations of holographic negativity using 2D CFT techniques that assumedℤ_2kreplica symmetry and proposed that the negativity was related to the entanglement wedge cross section. In this paper, we resolve this issue by showing that in general holographic states, the saddles computing$$ {\mathcal{E}}^{(2k)} $$ $E^{\left(2k\right)}$indeed break theℤ_2kreplica symmetry. Our argument involves an identity relating$$ {\mathcal{E}}^{(2k)} $$ $E^{\left(2k\right)}$to thek-th Rényi entropy on subregionAB^∗in the doubled state$$ {\left.|{\rho}_{AB}\right\rangle}_{A{A}^{\ast }{BB}^{\ast }} $$ ${\left(,{\rho }_{\mathrm{AB}}\right)}_{A{A}^{\ast }{\mathrm{BB}}^{\ast }}$, from which we see that theℤ_2kreplica symmetry is broken down toℤ_k. Fork< 1, which includes the case of$$ \mathcal{E} $$ $E$(A:B) atk= 1/2, we use a modified cosmic brane proposal to derive a new holographic prescription for$$ {\mathcal{E}}^{(2k)} $$ $E^{\left(2k\right)}$and show that it is given by a new saddle with multiple cosmic branes anchored to subregionsAandBin the original state. Using our prescription, we reproduce known results for the PSSY model and show that our saddle dominates over previously proposed CFT calculations neark= 1. Moreover, we argue that theℤ_2ksymmetric configurations previously proposed are not gravitational saddles, unlike our proposal. Finally, we contrast holographic calculations with those arising from RTNs with non-maximally entangled links, demonstrating that the qualitative form of backreaction in such RTNs is different from that in gravity. 

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2. Modified supersymmetric indices in AdS3/CFT2

   https://doi.org/10.1007/JHEP01(2024)099  

   Ardehali, Arash Arabi; Krishna, Hare (January 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We consider the 𝒩 = (2, 2) AdS₃/CFT₂dualities proposed by Eberhardt, where the bulk geometry is AdS₃× (S³×T⁴)/ℤ_k, and the CFT is a deformation of the symmetric orbifold of the supersymmetric sigma modelT⁴/ℤ_k(withk= 2, 3, 4, 6). The elliptic genera of the two sides vanish due to fermionic zero modes, so for microstate counting applications one must consider modified supersymmetric indices. In an analysis similar to that of Maldacena, Moore, and Strominger for the standard 𝒩 = (4, 4) case ofT⁴, we study the appropriate helicity-trace index of the boundary CFTs. We encounter a strange phenomenon where a saddle-point analysis of our indices reproduces only a fraction (respectively$$ \frac{1}{2} $$ $\frac{1}{2}$,$$ \frac{2}{3} $$ $\frac{2}{3}$,$$ \frac{3}{4} $$ $\frac{3}{4}$,$$ \frac{5}{6} $$ $\frac{5}{6}$) of the Bekenstein-Hawking entropy of the associated macroscopic black branes. 

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3. Topologically charged BPS microstates in AdS3/CFT2

   https://doi.org/10.1007/JHEP03(2025)069  

   Ardehali, Arash Arabi; Krishna, Hare (March 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> In the standard$$ \mathcal{N} $$ $N$= (4, 4) AdS₃/CFT₂with sym^N(T⁴), as well as the$$ \mathcal{N} $$ $N$= (2, 2) Datta-Eberhardt-Gaberdiel variant with sym^N(T⁴/ℤ₂), supersymmetric index techniques have not been applied so far to the CFT states with target-space momentum or winding. We clarify that the difficulty lies in a central extension of the SUSY algebra in the momentum and winding sectors, analogous to the central extension on the Coulomb branch of 4d$$ \mathcal{N} $$ $N$= 2 gauge theories. We define modified helicity-trace indices tailored to the momentum and winding sectors, and use them for microstate counting of the corresponding bulk black holes. In the$$ \mathcal{N} $$ $N$= (4, 4) case we reproduce the microstate matching of Larsen and Martinec. In the$$ \mathcal{N} $$ $N$= (2, 2) case we resolve a previous mismatch with the Bekenstein-Hawking formula encountered in the topologically trivial sector by going to certain winding sectors. 

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4. Instanton contributions to the ABJM free energy from quantum M2 branes

   https://doi.org/10.1007/JHEP10(2023)029  

   Beccaria, M; Giombi, S; Tseytlin, A A (October 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> We present a quantum M2 brane computation of the instanton prefactor in the leading non-perturbative contribution to the ABJM 3-sphere free energy at largeNand fixed levelk. Using supersymmetric localization, such instanton contribution was found earlier to take the form$$ {F}^{inst}\left(N,k\right)=-{\left({\sin}^2\frac{2\pi }{k}\right)}^{-1}\exp \left(-2\pi \sqrt{\frac{2N}{k}}\right)+.\dots $$ $F^{\text{inst}}\left(N,k\right)=-{\left({sin}^2\frac{2\pi }{k}\right)}^{-1}exp\left(-2\pi \sqrt{\frac{2N}{k}}\right)+.\dots$The exponent comes from the action of an M2 brane instanton wrapped onS³/ℤ_k, which represents the M-theory uplift of the ℂP¹instanton in type IIA string theory on AdS₄× ℂP³. The IIA string computation of the leading largekterm in the instanton prefactor was recently performed in arXiv:2304.12340. Here we find that the exact value of the prefactor$$ {\left({\sin}^2\frac{2\pi }{k}\right)}^{-1} $$ ${\left({sin}^2\frac{2\pi }{k}\right)}^{-1}$is reproduced by the 1-loop term in the M2 brane partition function expanded near theS³/ℤ_kinstanton configuration. As in the Wilson loop example in arXiv:2303.15207, the quantum M2 brane computation is well defined and produces a finite result in exact agreement with localization. 

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5. Scattering from (p, q)-strings in AdS5 × S5

   https://doi.org/10.1007/JHEP03(2025)181  

   Pufu, Silviu S; Rodriguez, Victor A; Wang, Yifan (March 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> Motivated by understanding the scattering of gravitons and their superpartners from extended (p,q)-strings in type IIB string theory via AdS/CFT, we study an integrated two-point function of stress tensor multiplet operators in the presence of a half-BPS line defect in$$ \mathcal{N} $$ $N$= 4 SU(N) super-Yang-Mills theory. We determine this integrated correlator at the five lowest non-trivial orders in$$ 1/\sqrt{N} $$ $1/\sqrt{N}$at fixed Yang-Mills coupling andθangle. Our calculations are performed explicitly when the line defect is a Wilson line, in which case we find a finite number of perturbative contributions at each order in$$ 1/\sqrt{N} $$ $1/\sqrt{N}$, as well as instanton contributions. Using SL(2,ℤ) transformations, our results can also be applied to Wilson-’t Hooft line defects dual to extended (p,q)-strings in the bulk. We analyze features of these integrated correlators in the weak coupling expansion by comparing with open-closed amplitudes of type IIB string theory on AdS₅× S⁵, as well as in its flat space limit. We predict new higher-derivative interaction vertices on the D1-brane and, more generally, on (p,q)-strings. 

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