ORCID Profile
0000-0001-7715-6175
Current Organisation
University of Melbourne
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Mathematical Aspects of Quantum and Conformal Field Theory, Quantum Gravity and String Theory | Mathematical Physics | Algebraic and Differential Geometry | Category Theory, K Theory, Homological Algebra | Integrable Systems (Classical and Quantum) | Pure Mathematics
Publisher: International Press of Boston
Date: 2010
Publisher: Hindawi Limited
Date: 2011
DOI: 10.1155/2011/513436
Abstract: We discuss recent constructions of global F-theory GUT models and explain how to make use of toric geometry to do calculations within this framework. After introducing the basic properties of global F-theory GUTs, we give a self-contained review of toric geometry and introduce all the tools that are necessary to construct and analyze global F-theory models. We will explain how to systematically obtain a large class of compact Calabi-Yau fourfolds which can support F-theory GUTs by using the software package PALP.
Publisher: Springer Science and Business Media LLC
Date: 07-2019
Abstract: We test the refined sw land distance conjecture in the Kähler moduli space of exotic one-parameter Calabi-Yaus. We focus on ex les with pseudo-hybrid points. These points, whose properties are not well-understood, are at finite distance in the moduli space. We explicitly compute the lengths of geodesics from such points to the large volume regime and show that the refined sw land distance conjecture holds. To compute the metric we use the sphere partition function of the gauged linear sigma model. We discuss several ex les in detail, including one ex le associated to a gauged linear sigma model with non-abelian gauge group.
Publisher: Springer Science and Business Media LLC
Date: 25-05-2006
Publisher: Springer Science and Business Media LLC
Date: 05-2017
Publisher: Elsevier BV
Date: 09-2007
Publisher: Springer Science and Business Media LLC
Date: 12-2019
Abstract: In this work we give a gauged linear sigma model (GLSM) realization of pairs of homologically projective dual Calabi-Yaus that have recently been constructed in the mathematics literature. Many of the geometries can be realized mathematically in terms of joins. We discuss how joins can be described in terms of GLSMs and how the associated Calabi-Yaus arise as phases in the GLSMs. Due to strong-coupling phenomena in the GLSM, the geometries are realized via a mix of perturbative and non-perturbative effects. We apply two-dimensional gauge dualities to construct dual GLSMs. Geometries that are realized perturbatively in one GLSM, are realized non-perturbatively in the dual, and vice versa.
Publisher: Springer Science and Business Media LLC
Date: 20-03-2007
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 2013
DOI: 10.4171/OWR/2013/44
Publisher: Springer Science and Business Media LLC
Date: 09-05-2022
DOI: 10.1007/S00220-022-04399-6
Abstract: The sphere partition function of Calabi–Yau gauged linear sigma models (GLSMs) has been shown to compute the exact Kähler potential of the Kähler moduli space of a Calabi–Yau. We propose a universal expression for the sphere partition function evaluated in hybrid phases of Calabi–Yau GLSMs that are fibrations of Landau–Ginzburg orbifolds over some base manifold. Special cases include Calabi–Yau complete intersections in toric ambient spaces and Landau–Ginzburg orbifolds. The key ingredients that enter the expression are Givental’s I / J -functions, the Gamma class and further data associated to the hybrid model. We test the proposal for one- and two-parameter abelian GLSMs, making connections, where possible, to known results from mirror symmetry and FJRW theory.
Publisher: International Press of Boston
Date: 2017
Publisher: Springer Science and Business Media LLC
Date: 11-2013
Publisher: International Press of Boston
Date: 2009
Publisher: Springer Science and Business Media LLC
Date: 04-2018
Abstract: In this paper we give gauged linear sigma model (GLSM) realizations of a number of geometries not previously presented in GLSMs. We begin by describing GLSM realizations of maps including Veronese and Segre embeddings, which can be applied to give GLSMs explicitly describing non-complete intersection constructions such as the intersection of one hypersurface with the image under some map of another. We also discuss GLSMs for intersections of Grassmannians and Pfaffians with one another, and with their images under various maps, which sometimes form exotic constructions of Calabi-Yaus, as well as GLSMs for other exotic Calabi-Yau constructions of Kanazawa. Much of this paper focuses on a specific set of ex les of GLSMs for intersections of Grassmannians G (2 , N ) with themselves after a linear rotation, including the Calabi-Yau case N = 5. One phase of the GLSM realizes an intersection of two Grassmannians, the other phase realizes an intersection of two Pfaffians. The GLSM has two nonabelian factors in its gauge group, and we consider dualities in those factors. In both the original GLSM and a double-dual, one geometric phase is realized perturbatively (as the critical locus of a superpotential), and the other via quantum effects. Dualizing on a single gauge group factor yields a model in which each geometry is realized through a simultaneous combination of perturbative and quantum effects.
Publisher: Springer Science and Business Media LLC
Date: 17-06-2004
Publisher: WORLD SCIENTIFIC
Date: 07-06-2012
DOI: 10.1142/8561
Publisher: Springer Science and Business Media LLC
Date: 07-2017
Publisher: WORLD SCIENTIFIC
Date: 12-2012
Publisher: Springer Science and Business Media LLC
Date: 03-2011
Publisher: Springer Science and Business Media LLC
Date: 10-2010
Publisher: Springer Science and Business Media LLC
Date: 07-2004
Publisher: Springer Science and Business Media LLC
Date: 09-05-2023
Abstract: We compute genus zero correlators of hybrid phases of Calabi-Yau gauged linear sigma models (GLSMs), i.e. of phases that are Landau-Ginzburg orbifolds fibered over some base. These correlators are generalisations of Gromov-Witten and FJRW invariants. Using previous results on the structure of the of the sphere- and hemisphere partition functions of GLSMs when evaluated in different phases, we extract the I -function and the J -function from a GLSM calculation. The J -function is the generating function of the correlators. We use the field theoretic description of hybrid models to identify the states that are inserted in these correlators. We compute the invariants for ex les of one- and two-parameter hybrid models. Our results match with results from mirror symmetry and FJRW theory.
Start Date: 2018
End Date: 2021
Funder: FWF Austrian Science Fund
View Funded ActivityStart Date: 12-2021
End Date: 12-2025
Amount: $395,311.00
Funder: Australian Research Council
View Funded ActivityStart Date: 05-2018
End Date: 05-2021
Amount: $446,340.00
Funder: Australian Research Council
View Funded ActivityStart Date: 01-2022
End Date: 01-2026
Amount: $673,820.00
Funder: Australian Research Council
View Funded Activity