Geometric Frameworks in String and Field Theories

Geometric methods underpin much of modern string and field theory, offering a unifying language to describe the rich tapestry of spacetime, gauge symmetries and dualities. Classical differential geometry provides the arena for general relativity and supergravity, while generalised geometric frameworks extend traditional notions of manifold, metric and connection to incorporate fluxes, branes and non-geometric backgrounds. Double and exceptional field theories elevate T- and U-dualities to manifest symmetries by introducing extended coordinates and generalised metrics, enabling simultaneous treatment of metric, B-field and higher-form fields. The α′ expansion introduces higher-derivative corrections that reshape curvature terms and gauge transformations, leading to novel non-perturbative solutions, from smooth cosmological bounces to de Sitter-like vacua in string cosmology. At the same time, algebraic structures such as Courant brackets and Poisson–Lie T-duality articulate the interplay between geometry and symmetry, while connections to M-theory and higher-dimensional supergravities are elegantly captured through exceptional groups. This geometric synthesis underpins advances in black hole physics, early universe cosmology and the quest for a consistent quantum theory of gravity.

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Geometric Frameworks in String and Field Theories publication trend

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

Technical terms

Generalised geometry: A framework extending tangent spaces by including form fields to unify diffeomorphisms and gauge symmetries.

Double field theory: A T-duality covariant formalism doubling coordinates to treat metric and B-field on an equal footing.

T-duality: A symmetry exchanging winding and momentum modes in string compactifications, relating large and small radii.

α′ corrections: Higher-derivative contributions in string effective actions arising from finite string length effects.

Dilaton: A scalar field controlling the string coupling, central to moduli stabilisation and cosmological dynamics.

References

1. β Symmetry of Supergravity. Physical Review Letters (2023).
2. Non-singular pre-big bang scenarios from all-order α′ corrections. Journal of High Energy Physics (2023).
3. Double field theory with matter and its cosmological application. Physical Review D (2023).
4. A hierarchy of WZW models related to super Poisson–Lie T-duality. European Physical Journal C (2024).