Symmetries of Calabi-Yau prepotentials with isomorphic flops

Article Mathematics, Applied

Flops for complete intersection Calabi-Yau threefolds

Callum Brodie et al.

Summary: In this paper, we study the flops of Calabi-Yau threefolds realized as Kahler-favourable complete intersections in products of projective spaces (CICYs) and identify two different types. The existence and type of the flops can be recognized from the configuration matrix of the CICY, and examples can be constructed based on this matrix.

JOURNAL OF GEOMETRY AND PHYSICS (2023)

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Article Mathematics, Applied

Flops, Gromov-Witten invariants and symmetries of line bundle cohomology on Calabi-Yau three-folds

Callum R. Brodie et al.

Summary: The zeroth line bundle cohomology on Calabi-Yau three-folds provides information about the existence of flop transitions and the genus zero Gromov-Witten invariants. We demonstrate this by studying various Picard number 2 Calabi-Yau three-folds realized as complete intersections in products of projective spaces. Many of these manifolds exhibit symmetries on the Picard lattice that preserve the zeroth cohomology.

JOURNAL OF GEOMETRY AND PHYSICS (2022)

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Article Physics, Particles & Fields

Geodesics in the extended Kahler cone of Calabi-Yau threefolds

Callum R. Brodie et al.

Summary: This article presents a detailed study of the effective cones of Calabi-Yau threefolds with h(1,1) = 2. It includes the possible types of walls bounding the Kahler cone and a classification of the intersection forms arising in the geometrical phases. The geodesic equation is explicitly solved for all three normal forms in the classification, and is used to analyze the evolution near Kahler cone walls and across flop transitions in the context of M-theory compactifications. Examples from the CICY and Kreuzer-Skarke lists are used to illustrate the structure of the extended Kahler and effective cones, providing a rich set of examples for studying topology change in string theory.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

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Article Physics, Particles & Fields

Superpotentials from singular divisors

Naomi Gendler et al.

Summary: We study Euclidean D3-branes wrapping divisors D in Calabi-Yau orientifold compactifications of type IIB string theory. We generalize the counting of fermion zero modes to singular divisors and establish the conditions for their contributions to the superpotential. We determine the exact effective cones and find that they have infinitely many generators. The resulting nonperturbative superpotentials are Jacobi theta functions.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

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Article Physics, Particles & Fields

Analytic structure of all loop banana integrals

Kilian Boenisch et al.

Summary: This research uses the Gelfand-Kapranov-Zelevinsk system to explore the primitive cohomology of a series of complete intersection Calabi-Yau manifolds, clarifying the analytic structure of all banana integrals with arbitrary masses. The study also determines the leading logarithmic structure and the imaginary part in the high energy regime, and provides closed-loop formulas and Picard-Fuchs differential equations for evaluating the integrals. Additionally, the study determines the value of the maximal cut equal mass four-loop integral using modular properties of the periods.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

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Article Astronomy & Astrophysics

Swampland conjectures and infinite flop chains

Callum R. Brodie et al.

Summary: The text discusses the swampland conjectures for M-theory compactified on Calabi-Yau threefolds and the situations where the moduli space has infinite discrete symmetry in cases involving a finite number of isomorphism classes of manifolds, as well as the scenario of infinite flop chains. The resolution of contradictions is achieved by dividing by this discrete symmetry.

PHYSICAL REVIEW D (2021)

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Article Physics, Particles & Fields