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1. Synthetic dimensions

   https://doi.org/10.1063/PT.3.5225  

   Hazzard, Kaden R.; Gadway, Bryce (April 2023, Physics Today)

   Novel geometries can be created using microwaves to couple the internal states of atoms or molecules and mimic movement in real space. 

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2. Rationality in four dimensions

   https://doi.org/10.1103/PhysRevD.109.105018  

   Rastelli, Leonardo; Rayhaun, Brandon C (May 2024, Physical Review D)

   By leveraging the physics of the Higgs branch, we argue that the conformal central charges $a$and $c$of an arbitrary 4D $\mathcal{N}=2$superconformal field theory (SCFT) are rational numbers. Our proof of the rationality of $c$is conditioned on a well-supported conjecture about how the Higgs branch of an SCFT is encoded in its protected chiral algebra. To establish the rationality of $a$, we further rely on a widely believed technical assumption on the high-temperature limit of the superconformal index. Published by the American Physical Society2024 

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3. Arakelov inequalities in higher dimensions

   https://doi.org/10.1515/crelle-2023-0075  

   Kovács, Sándor J; Taji, Behrouz (November 2023, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract We develop a Hodge theoretic invariant for families of projective manifolds that measures the potential failure of an Arakelov-type inequality in higher dimensions, one that naturally generalizes the classical Arakelov inequality over regular quasi-projective curves.We show that, for families of manifolds with ample canonical bundle, this invariant is uniformly bounded.As a consequence, we establish that such families over a base of arbitrary dimension satisfy the aforementioned Arakelov inequality, answering a question of Viehweg. 

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4. Learning knot invariants across dimensions

   https://doi.org/10.21468/SciPostPhys.14.2.021  

   Craven, Jessica; Hughes, Mark; Jejjala, Vishnu; Kar, Arjun (January 2023, SciPost Physics)

   We use deep neural networks to machine learn correlations betweenknot invariants in various dimensions. The three-dimensional invariantof interest is the Jones polynomial J(q) J ( q ) ,and the four-dimensional invariants are the Khovanov polynomial \text{Kh}(q,t) Kh ( q , t ) ,smooth slice genus g g ,and Rasmussen’s s s -invariant.We find that a two-layer feed-forward neural network can predict s s from \text{Kh}(q,-q^{-4}) Kh ( q , − q − 4 ) with greater than 99% 99 % accuracy. A theoretical explanation for this performance exists in knottheory via the now disproven knight move conjecture, which is obeyed byall knots in our dataset. More surprisingly, we find similar performancefor the prediction of s s from \text{Kh}(q,-q^{-2}) Kh ( q , − q − 2 ) ,which suggests a novel relationship between the Khovanov and Leehomology theories of a knot. The network predicts g g from \text{Kh}(q,t) Kh ( q , t ) with similarly high accuracy, and we discuss the extent to which themachine is learning s s as opposed to g g ,since there is a general inequality |s| ≤2g | s | ≤ 2 g .The Jones polynomial, as a three-dimensional invariant, is not obviouslyrelated to s s or g g ,but the network achieves greater than 95% 95 % accuracy in predicting either from J(q) J ( q ) .Moreover, similar accuracy can be achieved by evaluating J(q) J ( q ) at roots of unity. This suggests a relationship with SU(2) S U ( 2 ) Chern—Simons theory, and we review the gauge theory construction ofKhovanov homology which may be relevant for explaining the network’sperformance. 

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5. Landscape, Swampland and extra dimensions

   https://doi.org/10.22323/1.463.0215  

   Antoniadis, Ignatios; Anchordoqui, Luis A; Lüst, Dieter (July 2024, Sissa Medialab)