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

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## 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## References

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