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1. On invariants of modular categories beyond modular data

   https://doi.org/10.1016/j.jpaa.2018.12.017  

   Bonderson, Parsa; Delaney, Colleen; Galindo, César; Rowell, Eric C.; Tran, Alan; Wang, Zhenghan (September 2019, Journal of Pure and Applied Algebra)
2. Braided Zestings of Verlinde Modular Categories and Their Modular Data

   https://doi.org/10.1007/s00220-024-05097-1  

   Galindo, César; Mora, Giovanny; Rowell, Eric_C (October 2024, Communications in Mathematical Physics)

   Abstract Zesting of braided fusion categories is a procedure that can be used to obtain new modular categories from a modular category with non-trivial invertible objects. In this paper, we classify and construct all possible braided zesting data for modular categories associated with quantum groups at roots of unity. We produce closed formulas, based on the root system of the associated Lie algebra, for the modular data of these new modular categories. 

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3. Landscape of modular cosmology

   https://doi.org/10.1088/1475-7516/2025/05/037  

   Kallosh, Renata; Linde, Andrei (May 2025, Journal of Cosmology and Astroparticle Physics)

   Abstract We investigate the global structure of the recently discovered family of SL(2,ℤ)-invariant potentials describing inflationary α-attractors. These potentials have an inflationary plateau consisting of the fundamental domain and its images fully covering the upper part of the Poincaré half-plane. Meanwhile, the lower part of the half-plane is covered by an infinitely large number of ridges, which, at first glance, are too sharp to support inflation. However, we show that this apparent sharpness is just an illusion created by hyperbolic geometry, and each of these ridges is physically equivalent to the inflationary plateau in the upper part of the Poincaré half-plane. 

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4. Quantum extremal modular curvature: modular transport with islands

   https://doi.org/10.1007/JHEP10(2024)006  

   Aalsma, Lars; Keeler, Cynthia; Zukowski, Claire (October 2024, Journal of High Energy Physics)

   Modular Berry transport is a useful way to understand how geometric bulk information is encoded in the boundary CFT: the modular curvature is directly related to the bulk Riemann curvature. We extend this approach by studying modular transport in the presence of a non-trivial quantum extremal surface. Focusing on JT gravity on an AdS background coupled to a non-gravitating bath, we compute the modular curvature of an interval in the bath in the presence of an island: the Quantum Extremal Modular Curvature (QEMC). We highlight some important properties of the QEMC, most importantly that it is non-local in general. In an OPE limit, the QEMC becomes local and probes the bulk Riemann curvature in regions with an island. Our work gives a new approach to probe physics behind horizons. 

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5. Modular representations of exceptional supergroups

   https://doi.org/https://doi.org/10.1007/s00209-018-2098-x  

   Cheng, Shun-Jen; Shu, Bin; Wang, Weiqiang (April 2019, Mathematische Zeitschrift)

   We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed field of prime characteristic. 

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