Strong Coupling Dynamics of the Higgs Branch: Rolling a Higgs by Collapsing an Instanton

We construct the dual supergravity description of strongly coupled, large $N$, eight-supercharge gauge theories with fundamental hypermultiplets at points on the mixed Coulomb-Higgs branch. With certain assumptions about unknown couplings of D-branes to supergravity, this construction gives the correct metric on the hypermultiplet (Higgs-branch) component the moduli space, which decouples from the vector multiplet (Coulomb-branch) moduli. Going beyond the geodesic approximation, we find that the dynamics of a hypermultiplet VEV rolling towards a singularity on the Higgs component of the moduli space is sensitive to the vector multiplet moduli. The dual description of the approach to the singularity involves collapsing ``instantons'' of a non-Abelian Dirac-Born-Infeld theory in a curved background. In general, we find a decelerating approach to the singularity, although the manner of deceleration depends on the vector multiplet moduli. Upon introducing a potential on the Higgs branch of a four dimensional ${\cal N}=2$ theory coupled to gravity, this deceleration mechanism might lead to interesting inflating cosmologies analogous those studied recently by Alishahiha, Silverstein and Tong.