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1. 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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2. Thermodynamics of the near-extremal Kerr spacetime

   https://doi.org/10.1007/JHEP06(2024)011  

   Rakic, Ilija; Rangamani, Mukund; Turiaci, Gustavo J (June 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We examine the thermodynamics of a near-extremal Kerr black hole, and demonstrate that the geometry behaves as an ordinary quantum system with a vanishingly small degeneracy at low temperatures. This is in contrast with the classical analysis, which instead predicts a macroscopic entropy for the extremal Kerr black hole. Our results follow from a careful analysis of the gravitational path integral. Specifically, the low temperature canonical partition function behaves as$$ Z\sim {T}^{\frac{3}{2}}\ {e}^{S_0+c\log {S}_0} $$ $Z\sim T^{\frac{3}{2}}{e}^{S_0+clog{S}_0}$, withS₀the classical degeneracy andca numerical coefficient we compute. This is in line with the general expectations for non-supersymmetric near-extremal black hole thermodynamics, as has been clarified in the recent past, although cases without spherical symmetry have not yet been fully analyzed until now. We also point out some curious features relating to the rotational zero modes of the near-extremal Kerr black hole background that affects the coefficientc. This raises a puzzle when considering similar black holes in string theory. Our results generalize to other rotating black holes, as we briefly exemplify. 

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3. Notes on gauging noninvertible symmetries. Part I. Multiplicity-free cases

   https://doi.org/10.1007/JHEP02(2024)154  

   Perez-Lona, A; Robbins, D; Sharpe, E; Vandermeulen, T; Yu, X (February 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions. We specialize to certain gaugeable cases, specifically, fusion categories of the form$$ \textrm{Rep}\left(\mathcal{H}\right) $$ $\mathrm{Rep}\left(H\right)$for$$ \mathcal{H} $$ $H$a suitable Hopf algebra (which includes the special case Rep(G) forGa finite group). We also specialize to the case that the fusion category is multiplicity-free. We discuss how to construct a modular-invariant partition function from a choice of Frobenius algebra structure on$$ {\mathcal{H}}^{\ast } $$ $H^{\ast }$. We discuss how ordinaryGorbifolds for finite groupsGare a special case of the construction, corresponding to the fusion category Vec(G) = Rep(ℂ[G]^*). For the cases Rep(S₃), Rep(D₄), and Rep(Q₈), we construct the crossing kernels for general intertwiner maps. We explicitly compute partition functions in the examples of Rep(S₃), Rep(D₄), Rep(Q₈), and$$ \textrm{Rep}\left({\mathcal{H}}_8\right) $$ $\mathrm{Rep}\left(H_8\right)$, and discuss applications inc= 1 CFTs. We also discuss decomposition in the special case that the entire noninvertible symmetry group acts trivially. 

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4. Refined Chabauty–Kim computations for the thrice-punctured line over $$\mathbb {Z}[1/6]$$

   https://doi.org/10.1007/s40993-024-00597-4  

   Lüdtke, Martin (March 2025, Research in Number Theory)

   Abstract The Chabauty–Kim method and its refined variant by Betts and Dogra aim to cut out theS-integral points$$X(\mathbb {Z}_S)$$ $X\left(Z_S\right)$on a curve inside thep-adic points$$X(\mathbb {Z}_p)$$ $X\left(Z_p\right)$by producing enough Coleman functions vanishing on them. We derive new functions in the case of the thrice-punctured line whenScontains two primes. We describe an algorithm for computing refined Chabauty–Kim loci and verify Kim’s Conjecture over$$\mathbb {Z}[1/6]$$ $Z[1/6]$for all choices of auxiliary prime $$p < 10{,}000$$ $p<10,000$. 

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5. Measurement of the τ lepton polarization in Z boson decays in proton-proton collisions at $$ \sqrt{s} $$ = 13 TeV

   https://doi.org/10.1007/JHEP01(2024)101  

   Hayrapetyan, A; Tumasyan, A; Adam, W; Andrejkovic, J W; Bergauer, T; Chatterjee, S; Damanakis, K; Dragicevic, M; Escalante_Del_Valle, A; Hussain, P S; et al (January 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> The polarization ofτleptons is measured using leptonic and hadronicτlepton decays in Z →τ⁺τ⁻events in proton-proton collisions at$$ \sqrt{s} $$ $\sqrt{s}$= 13 TeV recorded by CMS at the CERN LHC with an integrated luminosity of 36.3 fb⁻¹. The measuredτ⁻lepton polarization at the Z boson mass pole is$$ {\mathcal{P}}_{\tau}\left(\textrm{Z}\right) $$ $P_{\tau }\left(Z\right)$= −0.144 ± 0.006 (stat) ± 0.014 (syst) = −0.144 ± 0.015, in good agreement with the measurement of theτlepton asymmetry parameter ofA_τ= 0.1439 ± 0.0043 =$$ -{\mathcal{P}}_{\tau}\left(\textrm{Z}\right) $$ $-P_{\tau }\left(Z\right)$at LEP. Theτlepton polarization depends on the ratio of the vector to axial-vector couplings of theτleptons in the neutral current expression, and thus on the effective weak mixing angle sin²$$ {\theta}_{\textrm{W}}^{\textrm{eff}} $$ ${\theta }_W^{\mathrm{eff}}$, independently of the Z boson production mechanism. The obtained value sin²$$ {\theta}_{\textrm{W}}^{\textrm{eff}} $$ ${\theta }_W^{\mathrm{eff}}$= 0.2319 ± 0.0008(stat) ± 0.0018(syst) = 0.2319 ± 0.0019 is in good agreement with measurements ate⁺e⁻colliders. 

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