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1. Dimension-eight operator basis for universal standard model effective field theory

   https://doi.org/10.1103/PhysRevD.110.033003  

   Corbett, Tyler; Desai, Jay; Éboli, O_J P; Gonzalez-Garcia, M C (August 2024, Physical Review D)

   We present the basis of dimension-eight operators associated with universal theories. We first derive a complete list of independent dimension-eight operators formed with the Standard Model bosonic fields characteristic of such universal new physics scenarios. Without imposing C or P symmetries the basis contains 175 operators—that is, the assumption of universality reduces the number of independent Standard Model effective field theory (SMEFT) coefficients at dimension eight from 44807 to 175. 89 of the 175 universal operators are included in the general dimension-eight operator basis in the literature. The 86 additional operators involve higher derivatives of the Standard Model bosonic fields and can be rotated in favor of operators involving fermions using the Standard Model equations of motion for the bosonic fields. By doing so we obtain the allowed fermionic operators generated in this class of models which we map into the corresponding 86 independent combinations of operators in the dimension-eight basis of [C. W. Murphy, Dimension-8 operators in the standard model effective field theory, .]. Published by the American Physical Society2024 

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2. The essential dimension of congruence covers

   https://doi.org/10.1112/S0010437X21007594  

   Farb, Benson; Kisin, Mark; Wolfson, Jesse (November 2021, Compositio Mathematica)

   Abstract Consider the algebraic function $$\Phi _{g,n}$$ that assigns to a general $$g$$ -dimensional abelian variety an $$n$$ -torsion point. A question first posed by Klein asks: What is the minimal $$d$$ such that, after a rational change of variables, the function $$\Phi _{g,n}$$ can be written as an algebraic function of $$d$$ variables? Using techniques from the deformation theory of $$p$$ -divisible groups and finite flat group schemes, we answer this question by computing the essential dimension and $$p$$ -dimension of congruence covers of the moduli space of principally polarized abelian varieties. We apply this result to compute the essential $$p$$ -dimension of congruence covers of the moduli space of genus $$g$$ curves, as well as its hyperelliptic locus, and of certain locally symmetric varieties. These results include cases where the locally symmetric variety $$M$$ is proper . As far as we know, these are the first examples of nontrivial lower bounds on the essential dimension of an unramified, nonabelian covering of a proper algebraic variety. 

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3. Weyl cycles on the blow up of P^4 at eight points

   https://doi.org/10.1007/978-3-031-11938-5_1  

   Brambilla, M Chiara; Dumitrescu, Olivia; Postinghel, Elisa (May 2024, Trends in mathematics)

   We define the Weyl cycles on X_n^ s , the blown-up projective space P^n in s points in general position. In particular, we focus on the Mori Dream spaces X3 7 and X4 8, where we classify all the Weyl cycles of codimension two. We further introduce the Weyl expected dimension for the space of global sections of any effective divisor that generalizes the linear expected dimension of [ 2] and the secant expected dimension of [ 4]. 

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4. Astrophysical constraints on decaying dark gravitons

   https://doi.org/10.1007/JHEP06(2024)047  

   Law-Smith, Jamie_A P; Obied, Georges; Prabhu, Anirudh; Vafa, Cumrun (June 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In the dark dimension scenario, which predicts an extra dimension of micron scale, dark gravitons (KK modes) are a natural dark matter candidate. In this paper, we study observable features of this model. In particular, their decay to standard matter fields can distort the CMB and impact other astrophysical signals. Using this we place bounds on the parameters of this model. In particular we find that the natural range of parameters in this scenario is consistent with these constraints and leads to the prediction that the mean mass of the dark matter today is close to a few hundred keV and the effective size of the extra dimension is around 1–30 μm. 

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5. Level repulsion in $$ \mathcal{N} $$ = 4 super-Yang-Mills via integrability, holography, and the bootstrap

   https://doi.org/10.1007/JHEP07(2024)059  

   Chester, Shai M; Dempsey, Ross; Pufu, Silviu S (July 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We combine supersymmetric localization with the numerical conformal bootstrap to bound the scaling dimension and OPE coefficient of the lowest-dimension unprotected operator in$$ \mathcal{N} $$ $N$= 4 SU(N) super-Yang-Mills theory for a wide range ofNand Yang-Mills couplingsg_YM. We find that our bounds are approximately saturated by weak coupling results at smallg_YM. Furthermore, at largeNour bounds interpolate between integrability results for the Konishi operator at smallg_YMand strong-coupling results, including the first few stringy corrections, for the lowest-dimension double-trace operator at largeg_YM. In particular, our scaling dimension bounds describe the level splitting between the single- and double-trace operators at intermediate coupling. 

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