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1. Higher-group symmetry of (3+1)D fermionic $$\mathbb{Z}_2$$ gauge theory: Logical CCZ, CS, and T gates from higher symmetry

   https://doi.org/10.21468/SciPostPhys.16.5.122  

   Barkeshli, Maissam; Hsin, Po-Shen; Kobayashi, Ryohei (January 2024, SciPost Physics)

   It has recently been understood that the complete global symmetry of finite group topological gauge theories contains the structure of a higher-group. Here we study the higher-group structure in (3+1)D\mathbb{Z}_2 ${\mathbb{Z}}_2$gauge theory with an emergent fermion, and point out that pumping chiralp+ip $p+ip$topological states gives rise to a\mathbb{Z}_{8} ${\mathbb{Z}}_8$0-form symmetry with mixed gravitational anomaly. This ordinary symmetry mixes with the other higher symmetries to form a 3-group structure, which we examine in detail. We then show that in the context of stabilizer quantum codes, one can obtain logical CCZ and CS gates by placing the code on a discretization ofT^3 $T^3$(3-torus) andT^2 \rtimes_{C_2} S^1 $T^2{⋊}_{C_2}{S}^1$(2-torus bundle over the circle) respectively, and pumpingp+ip $p+ip$states. Our considerations also imply the possibility of a logicalT $T$gate by placing the code on\mathbb{RP}^3 ${ℝ\mathbb{P}}^3$and pumping ap+ip $p+ip$topological state. 

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2. More accurate $$ \sigma \left(\mathcal{GG}\to h\right),\Gamma \left(h\to \mathcal{GG},\mathcal{AA},\overline{\Psi}\Psi \right) $$ and Higgs width results via the geoSMEFT

   https://doi.org/10.1007/JHEP01(2024)170  

   Martin, Adam; Trott, Michael (January 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We develop Standard Model Effective Field Theory (SMEFT) predictions ofσ($$ \mathcal{GG} $$ $\mathrm{GG}$→h), Γ(h→$$ \mathcal{GG} $$ $\mathrm{GG}$), Γ(h→$$ \mathcal{AA} $$ $\mathrm{AA}$) to incorporate full two loop Standard Model results at the amplitude level, in conjunction with dimension eight SMEFT corrections. We simultaneously report consistent Γ(h→$$ \overline{\Psi}\Psi $$ $\overline{\Psi }\Psi$) results including leading QCD corrections and dimension eight SMEFT corrections. This extends the predictions of the former processes Γ, σto a full set of corrections at$$ \mathcal{O}\left({\overline{v}}_T^2/{\varLambda}^2{\left(16{\pi}^2\right)}^2\right) $$ $O\left({\overline{v}}_T^2/{\Lambda }^2{\left(16{\pi }^2\right)}^2\right)$and$$ \mathcal{O}\left({\overline{v}}_T^4/{\Lambda}^4\right) $$ $O\left({\overline{v}}_T^4/{\Lambda }^4\right)$, where$$ {\overline{v}}_T $$ ${\overline{v}}_T$is the electroweak scale vacuum expectation value and Λ is the cut off scale of the SMEFT. Throughout, cross consistency between the operator and loop expansions is maintained by the use of the geometric SMEFT formalism. For Γ(h→$$ \overline{\Psi}\Psi $$ $\overline{\Psi }\Psi$), we include results at$$ \mathcal{O}\left({\overline{v}}_T^2/{\Lambda}^2\left(16{\pi}^2\right)\right) $$ $O\left({\overline{v}}_T^2/{\Lambda }^2\left(16{\pi }^2\right)\right)$in the limit where subleadingm_Ψ→ 0 corrections are neglected. We clarify how gauge invariant SMEFT renormalization counterterms combine with the Standard Model counter terms in higher order SMEFT calculations when the Background Field Method is used. We also update the prediction of the total Higgs width in the SMEFT to consistently include some of these higher order perturbative effects. 

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3. The half-volume spectrum of a manifold

   https://doi.org/10.1007/s00526-025-02949-z  

   Mazurowski, Liam; Zhou, Xin (May 2025, Calculus of Variations and Partial Differential Equations)

   Abstract We define the half-volume spectrum$$\{{\tilde{\omega }_p\}_{p\in \mathbb {N}}}$$ $\{{\tilde{\omega }}_p{\}}_{p\in N}$of a closed manifold$$(M^{n+1},g)$$ $(M^{n+1},g)$. This is analogous to the usual volume spectrum ofM, except that we restrict top-sweepouts whose slices each enclose half the volume ofM. We prove that the Weyl law continues to hold for the half-volume spectrum. We define an analogous half-volume spectrum$$\tilde{c}(p)$$ $\tilde{c}\left(p\right)$in the phase transition setting. Moreover, for$$3 \le n+1 \le 7$$ $3\le n+1\le 7$, we use the Allen–Cahn min-max theory to show that each$$\tilde{c}(p)$$ $\tilde{c}\left(p\right)$is achieved by a constant mean curvature surface enclosing half the volume ofMplus a (possibly empty) collection of minimal surfaces with even multiplicities. 

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4. Intersections of dual 𝑆𝐿₃-webs

   https://doi.org/10.1090/tran/9349  

   Shen, Linhui; Sun, Zhe; Weng, Daping (August 2025, Transactions of the American Mathematical Society)

   We introduce a topological intersection number for an ordered pair of ${\mathrm{SL}}_3$-webs on a decorated surface. Using this intersection pairing between reduced $({\mathrm{SL}}_3,\mathcal{A})$-webs and a collection of $({\mathrm{SL}}_3,\mathcal{X})$-webs associated with the Fock–Goncharov cluster coordinates, we provide a natural combinatorial interpretation of the bijection from the set of reduced $({\mathrm{SL}}_3,\mathcal{A})$-webs to the tropical set ${\mathcal{A}}_{{\mathrm{PGL}}_3,\stackrel{^<\#comment/>}{S}}^{+}\left({\mathbb{Z}}^t\right)$, as established by Douglas and Sun in [Forum Math. Sigma 12 (2024), p. e5, 55]. We provide a new proof of the flip equivariance of the above bijection, which is crucial for proving the Fock–Goncharov duality conjecture of higher Teichmüller spaces for ${\mathrm{SL}}_3$. 

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5. Search for leptoquark pair production decaying into $$te^- \bar{t}e^+$$ or $$t\mu ^- \bar{t}\mu ^+$$ in multi-lepton final states in pp collisions at $$\sqrt{s} = 13\,\textrm{TeV}$$ with the ATLAS detector

   https://doi.org/10.1140/epjc/s10052-024-12975-4  

   Aad, G; Abbott, B; Abbott, D C; Abeling, K; Abidi, S H; Aboulhorma, A; Abramowicz, H; Abreu, H; Abulaiti, Y; Hoffman, A_C Abusleme; et al (August 2024, The European Physical Journal C)

   Abstract A search for leptoquark pair production decaying into$$te^- \bar{t}e^+$$ $t{e}^{-}\overline{t}{e}^{+}$or$$t\mu ^- \bar{t}\mu ^+$$ $t{\mu }^{-}\overline{t}{\mu }^{+}$in final states with multiple leptons is presented. The search is based on a dataset ofppcollisions at$$\sqrt{s}=13~\text {TeV} $$ $\sqrt{s}=13\text{TeV}$recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 139 fb$$^{-1}$$ $_{}^{-1}$. Four signal regions, with the requirement of at least three light leptons (electron or muon) and at least two jets out of which at least one jet is identified as coming from ab-hadron, are considered based on the number of leptons of a given flavour. The main background processes are estimated using dedicated control regions in a simultaneous fit with the signal regions to data. No excess above the Standard Model background prediction is observed and 95% confidence level limits on the production cross section times branching ratio are derived as a function of the leptoquark mass. Under the assumption of exclusive decays into$$te^{-}$$ $t{e}^{-}$($$t\mu ^{-}$$ $t{\mu }^{-}$), the corresponding lower limit on the scalar mixed-generation leptoquark mass$$m_{\textrm{LQ}_{\textrm{mix}}^{\textrm{d}}}$$ $m_{{\text{LQ}}_{\text{mix}}^{\text{d}}}$is at 1.58 (1.59) TeV and on the vector leptoquark mass$$m_{{\tilde{U}}_1}$$ $m_{{\tilde{U}}_1}$at 1.67 (1.67) TeV in the minimal coupling scenario and at 1.95 (1.95) TeV in the Yang–Mills scenario. 

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