BPS open strings and A-D-E-singularities in F-theory on K3

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Article

Abstract

We improve on a recently constructed graphical representation of the supergravity 7-brane solution and apply this refined representation to re-study the open string description of the A-D-E-singularities in F-theory on K3. A noteworthy feature of the graphical representation is that it provides the complete global branch cut structure of the 7-brane solution which plays an important role in our analysis. We first identify those groups of branes which when made to coincide lead to the A-D-E-gauge groups. We next show that there is always a sufficient number of open BPS strings to account for all the generators of the gauge group. However, as we will show, there is in general no one-to-one relation between BPS strings and gauge group generators.

For the \( {D_{n + {4^{-} }}} \) and E-singularities, in order to relate BPS strings with gauge group generators, we make an SU(n + 4), respectively SU(5) subgroup of the \( {D_{n + {4^{-} }}} \) and E-gauge groups manifest. We find that only for the D-series (and for the standard A-series) this is sufficient to identify, in a one-to-one manner, which BPS strings correspond to which gauge group generators.

Keywords

F-Theory D-branes Discrete and Finite Symmetries 

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© The Author(s) 2010

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

Authors and Affiliations

  1. 1.Centre for Theoretical PhysicsUniversity of GroningenGroningenThe Netherlands
  2. 2.Albert Einstein Center for Fundamental Physics, Institute for Theoretical PhysicsUniversity of BernBernSwitzerland

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