Beyond large complex structure: quantized periods and boundary data for one-modulus singularities

A bstract We study periods in an integral basis near all possible singularities in one-dimensional complex structure moduli spaces of Calabi-Yau threefolds. Near large complex structure points these asymptotic periods are well understood in terms of the topological data of the mirror Calabi-Yau mani...

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Published in:The journal of high energy physics Vol. 2024; no. 7; pp. 151 - 109
Main Authors: Bastian, Brice, van de Heisteeg, Damian, Schlechter, Lorenz
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 17.07.2024
Springer Nature B.V
SpringerOpen
Subjects:
Classical and Quantum Gravitation
Couplings
Differential and Algebraic Geometry
Effective Field Theories
Elementary Particles
Geometry
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Singularity (mathematics)
String Theory
Supergravity
Superstring Vacua
Topology
Effective Field Theories
Superstring Vacua
Differential and Algebraic Geometry
ISSN:1029-8479, 1029-8479
Online Access:Get full text
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Summary:A bstract We study periods in an integral basis near all possible singularities in one-dimensional complex structure moduli spaces of Calabi-Yau threefolds. Near large complex structure points these asymptotic periods are well understood in terms of the topological data of the mirror Calabi-Yau manifold. The aim of this work is to characterize the period data near other boundaries in moduli space such as conifold and K-points. Using results from Hodge theory, we provide the general form of these periods in a quantized three-cycle basis. Based on these periods we compute the prepotential and related physical couplings of the underlying supergravity theory. Moreover, we elucidate the meaning of the model-dependent coefficients that appear in these expressions: these can be identified with certain topological and arithmetic numbers associated to the singular geometry at the moduli space boundary. We illustrate our findings by studying a wide set of examples.
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP07(2024)151