Gauge Fields & Higher Dimensions

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Abstractions about gauge and Yang–Mills theories, string dualities, unification, extra dimensions, amplitudes, and discrete models of fundamental spacetime.

9 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Amplituhedron — A positive geometric object whose canonical differential form encodes scattering amplitudes in planar maximally supersymmetric Yang–Mills theory without making locality and unitarity manifest inputs.
• Dimensional deconstruction — A four-dimensional gauge-theory construction whose product groups and link fields reproduce a discretized extra dimension over an energy range.
• Extra dimensions — Hypothesized spatial or temporal dimensions beyond the observed three spatial dimensions and one time dimension, used in higher-dimensional physical theories.
• Gauge theory — A field theory whose action is invariant under spacetime-dependent transformations from a gauge group, requiring connection-like gauge fields that relate local choices and whose curvature represents physical field strength.
• Grand Unified Theory — A particle-physics model that embeds the strong, weak and electromagnetic gauge interactions in one larger gauge symmetry at high energy.
• String duality — Relate apparently different string-theory descriptions as equivalent formulations of the same physics, mapping spectra, couplings, compactification data, and observables across weak/strong, large/small, or geometric/nongeometric regimes.
• String theory — A quantum-gravity framework in which fundamental excitations are one-dimensional strings whose vibrational states and interactions generate particle species, forces and spacetime-dependent spectra.
• World crystal — A speculative spacetime model representing the Planck-scale vacuum as a crystal-like lattice whose defects and elastic responses reproduce gravitational geometry.
• Yang–Mills theory — A non-Abelian gauge-field theory in which a connection on a principal bundle has curvature dynamics derived from the Yang–Mills action.