Heterotic phase transitions and singularities of the gauge dyonic string

Heterotic strings on R6 × K3 generically appear to undergo some interesting new phase transition at that value of the string coupling for which one of the six-dimensional gauge field kinetic energies changes sign. An exception is the E8 × E8 string with equal instanton numbers in the two E8ʹs, which admits a heterotic/heterotic self-duality. In this paper, we generalize the dyonic string solution of the six-dimensional heterotic string to include non-trivial gauge field configurations corresponding to self-dual Yang-Mills instantons in the four transverse dimensions. We find that vacua which undergo a phase transition always admit a string solution exhibiting a naked singularity, whereas for vacua admitting a self-duality the solution is always regular. When there is a phase transition, there exists a choice of instanton numbers for which the dyonic string is tensionless and quasi-anti-self-dual at that critical value of the coupling. For an infinite subset of the other choices of instanton number, the string will also be tensionless, but all at larger values of the coupling.