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Geometric engineering on flops of length two

Journal of High Energy Physics volume 2018, Article number: 90 (2018) Cite this article

Abstract

Type IIA on the conifold is a prototype example for engineering QED with one charged hypermultiplet. The geometry admits a flop of length one. In this paper, we study the next generation of geometric engineering on singular geometries, namely flops of length two such as Laufer’s example, which we affectionately think of as the conifold 2.0. Type IIA on the latter geometry gives QED with higher-charge states. In type IIB, even a single D3-probe gives rise to a nonabelian quiver gauge theory. We study this class of geometries explicitly by leveraging their quiver description, showing how to parametrize the exceptional curve, how to see the flop transition, and how to find the noncompact divisors intersecting the curve. With a view towards F-theory applications, we show how these divisors contribute to the enhancement of the Mordell-Weil group of the local elliptic fibration defined by Laufer’s example.

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Affiliations

  1. Service de Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050, Bruxelles, Belgium

    Andrés Collinucci

  2. Department of Physics, Technion, 32000, Haifa, Israel

    Marco Fazzi

  3. Department of Mathematics and Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, 31905, Haifa, Israel

    Marco Fazzi

  4. Dipartimento di Fisica, Università di Trieste, Strada Costiera 11, I-34151, Trieste, Italy

    Roberto Valandro

  5. INFN — Sezione di Trieste, Via Valerio 2, I-34127, Trieste, Italy

    Roberto Valandro

  6. The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I-34151, Trieste, Italy

    Roberto Valandro

Authors
  1. Andrés Collinucci
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  2. Marco Fazzi
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  3. Roberto Valandro
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Correspondence to Marco Fazzi.

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ArXiv ePrint: 1802.00813

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Collinucci, A., Fazzi, M. & Valandro, R. Geometric engineering on flops of length two. J. High Energ. Phys. 2018, 90 (2018). https://doi.org/10.1007/JHEP04(2018)090

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Keywords

  • D-branes
  • Differential and Algebraic Geometry
  • F-Theory
  • Brane Dynamics in Gauge Theories