Geometric Field Theories in Higher Dimensions

Geometric field theories in higher dimensions encompass a broad class of frameworks that extend the familiar four-dimensional description of spacetime to manifolds of greater dimensionality, often with the aim of unifying gravity with other fundamental interactions. These approaches draw on advances in differential geometry, topology and algebraic structures to formulate gauge fields, spinor fields and gravitational dynamics on spaces that may include compact internal dimensions, additional time coordinates or nonrelativistic limits. Classics such as Kaluza–Klein theory illustrated how electromagnetism may emerge from a five-dimensional metric, while modern string and M-theory exploit ten or eleven dimensions to accommodate supersymmetry and anomaly cancellation. Parallel developments in topological field theory and Chern–Simons constructions reveal how boundary phenomena and global properties of higher-dimensional manifolds govern quantum phases and dualities. More recently, expansions of Lie algebras have produced novel generalisations of Carroll, Newtonian and Galilean symmetries, yielding new gravity models that interpolate between relativistic and ultrarelativistic regimes. The global significance of this research lies in its potential to resolve long-standing puzzles in quantum gravity, cosmology and particle physics, while practical realisations emerge in condensed-matter analogues, holographic dualities and gravitational wave phenomenology. Interconnections between different geometric realisations continue to sharpen our understanding of renormalisability, anomaly structures and the role of torsion and curvature in unified field descriptions.

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Geometric Field Theories in Higher Dimensions publication trend

The graph below shows the total number of articles in geometric field theories in higher dimensions across all publications each year (not limited to Nature Index journals).

Technical terms

Higher-dimensional manifold: A space that generalises four-dimensional spacetime by including additional spatial or temporal dimensions, serving as the stage for extended field theories.

Gauge field: A geometric object associated with local symmetry transformations, mediating interactions by defining connections on principal bundles.

Spinor: An object transforming under spin groups, vital for representing fermionic degrees of freedom in curved or higher-dimensional contexts.

Rarita-Schwinger field: A spin-3/2 tensor–spinor field that generalises the Dirac formalism, central to supergravity and higher-spin models.

Carroll symmetry: A contraction of the Poincaré group obtained in the limit of vanishing light speed, giving rise to ultrarelativistic or “frozen” kinematics dual to nonrelativistic symmetries.

References

1. Massless Rarita-Schwinger equations: Half and three halves spin solution. SciPost Physics (2024).
2. Looking for Carroll particles in two time spacetime. Physical Review D (2024).
3. 3D Carrollian gravity from 2D Euclidean symmetry. European Physical Journal C (2025).