Recent Developments in Line Bundle Cohomology and Applications to String Phenomenology

Callum Brodie (), Andrei Constantin (), James Gray (), Andre Lukas () and Fabian Ruehle ()
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Callum Brodie: Robeson Hall, Virginia Tech, Department of Physics
Andrei Constantin: University of Oxford, Rudolf Peierls Centre for Theoretical Physics
James Gray: Robeson Hall, Virginia Tech, Department of Physics
Andre Lukas: University of Oxford, Rudolf Peierls Centre for Theoretical Physics
Fabian Ruehle: Northeastern University, Department of Physics & Department of Mathematics

A chapter in Nankai Symposium on Mathematical Dialogues, 2026, pp 79-92 from Springer

Abstract: Abstract Vector bundle cohomology represents a key ingredient for string phenomenology, being associated with the massless spectrum arising in string compactifications on smooth compact manifolds. Although standard algorithmic techniques exist for performing cohomology calculations, they are laborious and ill-suited for scanning over large sets of string compactifications to find those most relevant to particle physics. In this article (based on the second author’s lecture at the Nankai Symposium, August 2021) we review some recent progress in deriving closed-form expressions for line bundle cohomology and discuss some applications to string phenomenology.

Date: 2026
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DOI: 10.1007/978-981-19-2328-9_10

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