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Theoretical physicists working at a blackboard collaboration pod in the Beecroft building.
Credit: Jack Hobhouse

Prof Andre Lukas

Professor of Theoretical Physics, Head of Theoretical Physics

Research theme

  • Fundamental particles and interactions
  • Fields, strings, and quantum dynamics

Sub department

  • Rudolf Peierls Centre for Theoretical Physics

Research groups

  • Particle theory
Andre.Lukas@physics.ox.ac.uk
Telephone: 01865 (2)73953
Rudolf Peierls Centre for Theoretical Physics, room 70.11
  • About
  • Publications

Computation of quark masses from string theory

Nuclear Physics B Elsevier 1010 (2025) 116778

Authors:

Andrei Constantin, Cristofero S Fraser-Taliente, Thomas R Harvey, Andre Lukas, Burt Ovrut
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Fermion Masses and Mixing in String-Inspired Models

(2024)

Authors:

Andrei Constantin, Cristofero S Fraser-Taliente, Thomas R Harvey, Lucas TY Leung, Andre Lukas
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Enumerating Calabi‐Yau manifolds: placing bounds on the number of diffeomorphism classes in the Kreuzer‐Skarke list

Fortschritte der Physik Wiley 72:5 (2024) 2300264

Authors:

Aditi Chandra, Andrei Constantin, Cristofero Fraser-taliente, Thomas Harvey, Andre Lukas

Abstract:

The diffeomorphism class of simply connected smooth Calabi-Yau threefolds with torsion-free cohomology is determined via certain basic topological invariants: the Hodge numbers, the triple intersection form, and the second Chern class. In the present paper, we shed some light on this classification by placing bounds on the number of diffeomorphism classes present in the set of smooth Calabi-Yau threefolds constructed from the Kreuzer-Skarke (KS) list of reflexive polytopes up to Picard number six. The main difficulty arises from the comparison of triple intersection numbers and divisor integrals of the second Chern class up to basis transformations. By using certain basis-independent invariants, some of which appear here for the first time, we are able to place lower bounds on the number of classes. Upper bounds are obtained by explicitly identifying basis transformations, using constraints related to the index of line bundles. Extrapolating our results, we conjecture that the favorable entries of the KS list of reflexive polytopes lead to some (Formula presented.) diffeomorphically distinct Calabi-Yau threefolds.
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New Calabi–Yau manifolds from genetic algorithms

Physics Letters B Elsevier 850 (2024) 138504

Authors:

Per Berglund, Yang-Hui He, Elli Heyes, Edward Hirst, Vishnu Jejjala, Andre Lukas

Abstract:

Calabi–Yau manifolds can be obtained as hypersurfaces in toric varieties built from reflexive polytopes. We generate reflexive polytopes in various dimensions using a genetic algorithm. As a proof of principle, we demonstrate that our algorithm reproduces the full set of reflexive polytopes in two and three dimensions, and in four dimensions with a small number of vertices and points. Motivated by this result, we construct five-dimensional reflexive polytopes with the lowest number of vertices and points. By calculating the normal form of the polytopes, we establish that many of these are not in existing datasets and therefore give rise to new Calabi–Yau four-folds. In some instances, the Hodge numbers we compute are new as well.
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Computation of Quark Masses from String Theory

(2024)

Authors:

Andrei Constantin, Cristofero S Fraser-Taliente, Thomas R Harvey, Andre Lukas, Burt Ovrut
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