Geometric engineering on flops of length two

  • Andrés Collinucci
  • Marco Fazzi
  • Roberto Valandro
Open Access
Regular Article - Theoretical Physics
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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.

Keywords

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

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Service de Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay InstitutesBruxellesBelgium
  2. 2.Department of PhysicsTechnionHaifaIsrael
  3. 3.Department of Mathematics and Haifa Research Center for Theoretical Physics and AstrophysicsUniversity of HaifaHaifaIsrael
  4. 4.Dipartimento di FisicaUniversità di TriesteTriesteItaly
  5. 5.INFN — Sezione di TriesteTriesteItaly
  6. 6.The Abdus Salam International Centre for Theoretical PhysicsTriesteItaly

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