# Question about Duality between F-theory on elliptically fibered K3 and Heterotic/Type-I on T^2

I'm studying Sen's paper F-Theory and Orientifolds'' [arXiv:hep-th/9605150] where he discusses the duality between F-theory on an elliptically-fibered K3 and heterotic/type-I string theory on a two-torus $T^2$.

The basic idea is to go to a special point in the moduli space of K3, which corresponds to the orbifold limit of K3, i.e. at which K3 locally looks like $T^4/\mathbb{Z}_2$. At this point, it is further argued that the F-theory background reduces to a background in which the axion-dilaton modulus remains constant over the internal manifold of F-theory; so this limit can be identified with a particular orientifold of type-IIB theory, which in turn is T-dual to Type-I string theory on $T^2$.

So in conclusion, at the special point, F-theory on the (elliptically fibered) K3 is dual to Type-I string theory on $T^2$. Now by turning on appropriate background fields, one can deform the theories on each side of the duality away from the special point and one argues that the duality between the theories must hold at all points in the moduli space.

Now on page 3, Sen says

We also explicitly study deformations of the F-theory, as well as the orientifold theory, away from this special point in the moduli space. The moduli space of the orientifold theory is characterized by the vacuum expectation value of the Higgs field in the adjoint representation of the gauge group, or equivalently, locations of the sixteen seven-branes on the internal two dimensional manifold.

I realize I may be asking a question with a very obvious answer but what is the Higgs field and the adjoint representation here? Of what group?

• You should probably just read on. Check out the last paragraph on page 7, for instance. There is some $SO(8)$ gauge theory involved. – Danu Apr 29 '17 at 14:47