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1. Quantum electrodynamics of non-Hermitian Dirac fermions

   https://doi.org/10.1007/JHEP01(2024)143  

   Murshed, Sk Asrap; Roy, Bitan (January 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We develop an effective quantum electrodynamics for non-Hermitian (NH) Dirac materials interacting with photons. These systems are described by nonspatial symmetry protected Lorentz invariant NH Dirac operators, featuring two velocity parametersυ_Handυ_NHassociated with the standard Hermitian and a masslike anti-Hermitian Dirac operators, respectively. They display linear energy-momentum relation, however, in terms of an effective Fermi velocity$$ {\upsilon}_{\textrm{F}}=\sqrt{\upsilon_{\textrm{H}}^2-{\upsilon}_{\textrm{NH}}^2} $$ ${\upsilon }_F=\sqrt{{\upsilon }_H^2-{\upsilon }_{\mathrm{NH}}^2}$of NH Dirac fermions. Interaction with the fluctuating electromagnetic radiation then gives birth to an emergent Lorentz symmetry in this family of NH Dirac materials in the deep infrared regime, where the system possesses a unique terminal velocityυ_F=c, withcbeing the speed of light. While in two dimensions such a terminal velocity is set by the speed of light in the free space, dynamic screening in three spatial dimensions permits its nonuniversal values. Manifestations of such an emergent spacetime symmetry on the scale dependence of various physical observables in correlated NH Dirac materials are discussed. 

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2. The $$ {D}_3^{(2)} $$ spin chain and its finite-size spectrum

   https://doi.org/10.1007/JHEP11(2023)095  

   Frahm, Holger; Gehrmann, Sascha; Nepomechie, Rafael I.; Retore, Ana L. (November 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> Using the analytic Bethe ansatz, we initiate a study of the scaling limit of the quasi-periodic$$ {D}_3^{(2)} $$ $D_3^{\left(2\right)}$spin chain. Supported by a detailed symmetry analysis, we determine the effective scaling dimensions of a large class of states in the parameter regimeγ∈ (0,$$ \frac{\pi }{4} $$ $\frac{\pi }{4}$). Besides two compact degrees of freedom, we identify two independent continuous components in the finite-size spectrum. The influence of large twist angles on the latter reveals also the presence of discrete states. This allows for a conjecture on the central charge of the conformal field theory describing the scaling limit of the lattice model. 

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3. A QCD $R$ -axion

   https://doi.org/10.1103/PhysRevD.111.015048  

   Unwin, James; Yildirim, Tom (January 2025, Physical Review D)

   $R$-parity can be extended to a continuous global $\mathrm{U}(1{)}_R$symmetry. We investigate whether an anomalous $\mathrm{U}(1{)}_R$can be identified as the Peccei-Quinn symmetry suitable for solving the strong $CP$problem within supersymmetric extensions of the Standard Model. In this case, $\mathrm{U}(1{)}_R$is broken at some intermediate scale and the quantum chromodynamics axion is the $R$-axion. Moreover, the $R$-symmetry can potentially be gauged via the Green-Schwarz mechanism within completions to supergravity, in order to evade the axion quality problem. Obstacles to realizing this scenario are highlighted and phenomenologically viable approaches are identified. Published by the American Physical Society2025 

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4. Strong $CP$ and flavor in multi-Higgs theories

   https://doi.org/10.1103/rxml-5gd2  

   Hall, Lawrence; Manzari, Claudio Andrea; Noether, Bea (June 2025, Physical Review D)

   We introduce a class of multi-Higgs doublet extensions of the Standard Model that solve the strong $CP$problem with profound consequences for the flavor sector. The Yukawa matrices are constrained to have many zero entries by a “Higgs-flavor” symmetry, $G_{\mathrm{HF}}$, that acts on Higgs and quark fields. The violation of both $CP$and $G_{\mathrm{HF}}$occurs in the Higgs mass matrix so that, for certain choices of $G_{\mathrm{HF}}$charges, the strong $CP$parameter $\overline{\theta }$is zero at tree level. Radiative corrections to $\overline{\theta }$are computed in this class of theories. They vanish in realistic two-Higgs doublet models with $G_{\mathrm{HF}}={\mathbb{Z}}_3$. We also construct realistic three-Higgs models with $G_{\mathrm{HF}}=\mathrm{U}\left(1\right)$, where the one-loop results for $\overline{\theta }$are model-dependent. Requiring $\overline{\theta }<{10}^{-10}$has important implications for the flavor problem by constraining the Yukawa coupling and Higgs mass matrices. Contributions to $\overline{\theta }$from higher-dimension operators are computed at one loop and can also be sufficiently small, although the hierarchy problem of this class of theories is worse than in the Standard Model. 

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5. Solutions to the constant Yang–Baxter equation: additive charge conservation in three dimensions

   https://doi.org/10.1098/rspa.2023.0810  

   Hietarinta, J; Martin, P; Rowell, E C (July 2024, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   We find all solutions to the constant Yang–Baxter equation $R_{12}{R}_{13}{R}_{23}=R_{23}{R}_{13}{R}_{12}$in three dimensions, subject to an additive charge-conservation (ACC) ansatz. This ansatz is a generalization of (strict) charge-conservation, for which a complete classification in all dimensions was recently obtained. ACC introduces additional sector-coupling parameters—in three dimensions, there are four such parameters. In the generic dimension 3 case, in which all of the four parameters are non-zero, we find there is a single three parameter family of solutions. We give a complete analysis of this solution, giving the structure of the centralizer (symmetry) algebra in all orders. We also solve the remaining cases with three, two or one non-zero sector-coupling parameter(s). 

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