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1. Twistors, Hyper-Kaehler Manifolds, and Complex Moduli

   https://doi.org/10.1007/978-3-319-67519-0  

   LeBrun, Claude (November 2017, Springer INdAM series)

   Chiossi, Simon; Fino, Anna; Musso, Emilio; Podesta, Fabio; Vezzoni, Luigi (Ed.)

   A theorem of Kuranishi (Ann Math 75(2):536–577, 1962) tells us that the moduli space of complex structures on any smooth compact manifold is always locally a finite-dimensional space. Globally, however, this is simply not true; we display examples in which the moduli space contains a sequence of regions for which the local dimension tends to infinity. These examples naturally arise from the twistor theory of hyper-Kähler manifolds. 

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2. Three-loop effective potential for softly broken supersymmetry

   https://doi.org/10.1103/PhysRevD.109.015019  

   Martin, Stephen P (January 2024, Physical Review D)

   The effective potential has been previously calculated through three-loop order, in Landau gauge, for a general renormalizable theory using dimensional regularization. However, dimensional regularization is not appropriate for softly broken supersymmetric gauge theories, because it explicitly violates supersymmetry. In this paper, I obtain the three-loop effective potential using a supersymmetric regulator based on dimensional reduction. Checks follow from the vanishing of the effective potential in examples with supersymmetric vacua, and from renormalization scale invariance in examples for which supersymmetry is broken, either spontaneously or explicitly by soft terms. As byproducts, I obtain the three-loop Landau gauge anomalous dimension for the scalar component of a chiral supermultiplet, and the beta function for the field-independent vacuum energy. 

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3. Constructing operator basis in supersymmetry: a Hilbert series approach

   https://doi.org/10.1007/JHEP04(2023)097  

   Delgado, Antonio; Martin, Adam; Wang, Runqing (April 2023, Journal of High Energy Physics)

   A bstract In this paper we introduce a Hilbert series approach to build the operator basis for a N = 1 supersymmetry theory with chiral superfields. We give explicitly the form of the corrections that remove redundancies due to the equations of motion and integration by parts. In addition, we derive the maps between the correction spaces. This technique allows us to calculate the number of independent operators involving chiral and antichiral superfields to arbitrarily high mass dimension. Using this method, we give several illustrative examples. 

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4. Differentiable VQ-VAE's for Robust White Matter Streamline Encodings

   Lizarraga, A; Taraku, B; Honig, E; Wu, Y N; Joshi, S H (May 2024, IEEE International Symposium on Biomedical Imaging (ISBI))

   Given the complex geometry of white matter streamlines, Autoencoders have been proposed as a dimension-reduction tool to simplify the analysis streamlines in a low-dimensional latent spaces. However, despite these recent successes, the majority of encoder architectures only perform dimension reduction on single streamlines as opposed to a full bundle of streamlines. This is a severe limitation of the encoder architecture that completely disregards the global geometric structure of streamlines at the expense of individual fibers. Moreover, the latent space may not be well structured which leads to doubt into their interpretability. In this paper we propose a novel Differentiable Vector Quantized Variational Autoencoder, which are engineered to ingest entire bundles of streamlines as single data-point and provides reliable trustworthy encodings that can then be later used to analyze streamlines in the latent space. Comparisons with several state of the art Autoencoders demonstrate superior performance in both encoding and synthesis. 

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5. A Distance Conjecture for branes

   https://doi.org/10.1007/JHEP09(2025)155  

   Etheredge, Muldrow; Heidenreich, Ben; Rudelius, Tom (September 2025, Journal of High Energy Physics)

   We use branes to generalize the Distance Conjecture. We conjecture that in any infinite-distance limit in the moduli space of a d-dimensional quantum gravity theory, among the set of particle towers and fundamental branes with at most pmax spacetime dimensions (where pmax is an integer between 1 and d-2), at least one has mass/tension decreasing exponentially T ~ exp(–α ∆) with the moduli space distance ∆ at a rate of at least α ≥ 1/sqrt(d-pmax-1). Since pmax can vary, this represents multiple conditions, where the Sharpened Distance Conjecture is the pmax = 1 case. This conjecture is a necessary condition imposed on higher-dimensional theories in order for the Sharpened Distance Conjecture to hold in lower-dimensional theories. We test our conjecture in theories with maximal and half-maximal supersymmetry in diverse dimensions, finding that it is satisfied and often saturated. In some cases where it is saturated — most notably, heterotic string theory in 10 dimensions — we argue that novel, low-tension non-supersymmetric branes must exist. We also identify patterns relating the rates at which various brane tensions vary in infinite-distance limits and relate these tensions to the species scale. 

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