Long-range order for the fermion bilinear is proved in three Euclidean lattice Gross-Neveu models at small coupling and large even N via reflection positivity, chessboard estimates and a Peierls argument.
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Generalized BPS magnetic monopoles exist in inhomogeneous Yang-Mills-Higgs models with spatially varying couplings constrained to preserve the BPS bound, yielding exact solutions when the permeability exponent is 1 and a spectrum of compact, hollow, and multi-shell configurations otherwise.
Bi- and uni-vector deformations of heterotic supergravity solutions are constructed using gauged double field theory together with a generalized open/closed map.
Hodge loci in Calabi-Yau sigma models are identified with non-trivial categories of topological defects preserving N=(2,2) SCA and invertible on spectral-flow generators, with CM structure at special points.
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A two-parameter flow equation is derived for Anderson localization on the hyperbolic plane, with an extended critical line separating metallic and insulating phases in the plane of scale-dependent curvature and conductivity.
Asymmetric Pati–Salam Z2 actions in free-fermionic heterotic orbifolds yield 24 inequivalent moduli classes and induce doublet–triplet splitting independent of moduli stabilisation.
Minimal-doubling lattice fermion Hamiltonians yield single-Weyl phases when supplemented by a species-splitting mass term, but one-parameter symmetry-preserving deformations introduce additional Weyl nodes above a critical value.
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