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1. 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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2. Softening of a flat phonon mode in the kagome ScV6Sn6

   https://doi.org/10.1038/s41467-023-42186-6  

   Korshunov, A; Hu, H; Subires, D; Jiang, Y; Călugăru, D; Feng, X; Rajapitamahuni, A; Yi, C; Roychowdhury, S; Vergniory, M G; et al (December 2023, Nature Communications)

   Abstract Geometrically frustrated kagome lattices are raising as novel platforms to engineer correlated topological electron flat bands that are prominent to electronic instabilities. Here, we demonstrate a phonon softening at thek_z = πplane in ScV₆Sn₆. The low energy longitudinal phonon collapses at ~98 K andq = $$\frac{1}{3}\frac{1}{3}\frac{1}{2}$$ $\frac{1}{3}\frac{1}{3}\frac{1}{2}$due to the electron-phonon interaction, without the emergence of long-range charge order which sets in at a different propagation vectorq_CDW = $$\frac{1}{3}\frac{1}{3}\frac{1}{3}$$ $\frac{1}{3}\frac{1}{3}\frac{1}{3}$. Theoretical calculations corroborate the experimental finding to indicate that the leading instability is located at$$\frac{1}{3}\frac{1}{3}\frac{1}{2}$$ $\frac{1}{3}\frac{1}{3}\frac{1}{2}$of a rather flat mode. We relate the phonon renormalization to the orbital-resolved susceptibility of the trigonal Sn atoms and explain the approximately flat phonon dispersion. Our data report the first example of the collapse of a kagome bosonic mode and promote the 166 compounds of kagomes as primary candidates to explore correlated flat phonon-topological flat electron physics. 

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3. Bootstrapping M-theory orbifolds

   https://doi.org/10.1007/JHEP06(2024)001  

   Chester, Shai M; Pufu, Silviu S; Wang, Yifan; Yin, Xi (June 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We analyze correlation functions of SU(k) × SU(2)_Fflavor currents in a family of three-dimensional$$ \mathcal{N} $$ $N$= 4 superconformal field theories, combining analytic bootstrap methods with input from supersymmetric localization. Via holographic duality, we extract gluon and graviton scattering amplitudes of M-theory on AdS₄×S⁷/ℤ_kwhich contains a ℂ²/ℤ_korbifold singularity. From these results, we derive aspects of the effective description of M-theory on the orbifold singularity beyond its leading low energy limit. We also determine a threshold correction to the holographic correlator from the combined contribution of two-loop gluon and tree-level bulk graviton exchange. 

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4. Pole skipping in holographic theories with gauge and fermionic fields

   https://doi.org/10.1007/JHEP12(2023)084  

   Ning, Sirui; Wang, Diandian; Wang, Zi-Yue (December 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> Using covariant expansions, recent work showed that pole skipping happens in general holographic theories with bosonic fields at frequencies i(l_b−s)2πT, wherel_bis the highest integer spin in the theory andstakes all positive integer values. We revisit this formalism in theories with gauge symmetry and upgrade the pole-skipping condition so that it works without having to remove the gauge redundancy. We also extend the formalism by incorporating fermions with general spins and interactions and show that their presence generally leads to a separate tower of pole-skipping points at frequencies i(l_f−s)2πT,l_fbeing the highest half-integer spin in the theory andsagain taking all positive integer values. We also demonstrate the practical value of this formalism using a selection of examples with spins 0,$$ \frac{1}{2} $$ $\frac{1}{2}$,1,$$ \frac{3}{2} $$ $\frac{3}{2}$,2. 

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5. Negative moments of the Riemann zeta-function

   https://doi.org/10.1515/crelle-2023-0091  

   Bui, Hung M; Florea, Alexandra (January 2024, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract Assuming the Riemann Hypothesis, we study negative moments of the Riemann zeta-function and obtain asymptotic formulas in certain ranges of the shift in $\zeta \left(s\right)${\zeta(s)}. For example, integrating ${\left|\zeta \left(\frac{1}{2}+\alpha +it\right)\right|}^{-2k}${|\zeta(\frac{1}{2}+\alpha+it)|^{-2k}}with respect totfromTto $2T${2T}, we obtain an asymptotic formula when the shift α is roughly bigger than $\frac{1}{\log T}${\frac{1}{\log T}}and $k<\frac{1}{2}${k<\frac{1}{2}}. We also obtain non-trivial upper bounds for much smaller shifts, as long as $\log \frac{1}{\alpha }\ll \log \log T${\log\frac{1}{\alpha}\ll\log\log T}. This provides partial progress towards a conjecture of Gonek on negative moments of the Riemann zeta-function, and settles the conjecture in certain ranges. As an application, we also obtain an upper bound for the average of the generalized Möbius function. 

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