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1. Fully stabilized Minkowski vacua in the 26 Landau-Ginzburg model

   https://doi.org/10.1007/JHEP10(2024)095  

   Rajaguru, Muthusamy; Sengupta, Anindya; Wrase, Timm (October 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We study moduli stabilization via fluxes in the 2⁶Landau-Ginzburg model. Fluxes not only give masses to scalar fields but can also induce higher order couplings that stabilize massless fields. We investigate this for several different flux choices in the 2⁶model and find two examples that are inconsistent with the Refined Tadpole Conjecture. We also present, to our knowledge, the first 4d$$ \mathcal{N} $$ $N$= 1 Minkowski solution in string theory without any flat direction. 

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2. 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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3. Solutions of the Ginzburg–Landau equations with vorticity concentrating near a nondegenerate geodesic

   https://doi.org/10.4171/JEMS/1397  

   Colinet, Andrew; Jerrard, Robert; Sternberg, Peter (March 2025, Journal of the European Mathematical Society)

   It is well-known that under suitable hypotheses, for a sequence of solutions of the (simplified) Ginzburg–Landau equations-\Delta u_{\varepsilon} +\varepsilon^{-2}(|u_{\varepsilon}|^{2}-1)u_{\varepsilon} = 0, the energy and vorticity concentrate as\varepsilon\to 0around a codimension2stationary varifold – a (measure-theoretic) minimal surface. Much less is known about the question of whether, given a codimension2minimal surface, there exists a sequence of solutions for which the given minimal surface is the limiting concentration set. The corresponding question is very well-understood for minimal hypersurfaces and the scalar Allen–Cahn equation, and for the Ginzburg–Landau equations when the minimal surface is locally area-minimizing, but otherwise quite open. We consider this question on a3-dimensional closed Riemannian manifold(M,g), and we prove that any embedded nondegenerate closed geodesic can be realized as the asymptotic energy/ vorticity concentration set of a sequence of solutions of the Ginzburg–Landau equations. 

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4. Remarks on the existence of minimal models of log canonical generalized pairs

   https://doi.org/10.1007/s00209-024-03489-6  

   Tsakanikas, Nikolaos; Xie, Lingyao (April 2024, Mathematische Zeitschrift)

   Abstract Given an NQC log canonical generalized pair$$(X,B+M)$$ $(X,B+M)$whose underlying varietyXis not necessarily$$\mathbb {Q}$$ $Q$-factorial, we show that one may run a$$(K_X+B+M)$$ $(K_X+B+M)$-MMP with scaling of an ample divisor which terminates, provided that$$(X,B+M)$$ $(X,B+M)$has a minimal model in a weaker sense or that$$K_X+B+M$$ $K_X+B+M$is not pseudo-effective. We also prove the existence of minimal models of pseudo-effective NQC log canonical generalized pairs under various additional assumptions, for instance when the boundary contains an ample divisor. 

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5. A case study of SMEFT $$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ effects in diboson processes: pp → W±(ℓ±ν)γ

   https://doi.org/10.1007/JHEP05(2024)223  

   Martin, Adam (May 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In this paper we explorepp→W^±(ℓ^±ν)γto$$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ $O\left(1/{\Lambda }^4\right)$in the SMEFT expansion. Calculations to this order are necessary to properly capture SMEFT contributions that grow with energy, as the interference between energy-enhanced SMEFT effects at$$ \mathcal{O}\left(1/{\Lambda}^2\right) $$ $O\left(1/{\Lambda }^2\right)$and the Standard Model is suppressed. We find that there are several dimension eight operators that interfere with the Standard Model and lead to the same energy growth, ~$$ \mathcal{O}\left({E}^4/{\Lambda}^4\right) $$ $O\left(E^4/{\Lambda }^4\right)$, as dimension six squared. While energy-enhanced SMEFT contributions are a main focus, our calculation includes the complete set of$$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ $O\left(1/{\Lambda }^4\right)$SMEFT effects consistent with U(3)⁵flavor symmetry. Additionally, we include the decay of theW^±→ ℓ^±ν, making the calculation actually$$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ $\overline{q}{q}^{\prime }\to {\ell }^{\pm }\mathrm{\nu \gamma }$. As such, we are able to study the impact of non-resonant SMEFT operators, such as$$ \left({L}^{\dagger }{\overline{\sigma}}^{\mu }{\tau}^IL\right)\left({Q}^{\dagger }{\overline{\sigma}}^{\nu }{\tau}^IQ\right) $$ $\left(L^{†}{\overline{\sigma }}^{\mu }{\tau }^{I}L\right)\left(Q^{†}{\overline{\sigma }}^{\nu }{\tau }^{I}Q\right)$B_μν, which contribute to$$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ $\overline{q}{q}^{\prime }\to {\ell }^{\pm }\mathrm{\nu \gamma }$directly and not to$$ \overline{q}{q}^{\prime}\to {W}^{\pm}\gamma $$ $\overline{q}{q}^{\prime }\to W^{\pm }\gamma$. We show several distributions to illustrate the shape differences of the different contributions. 

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