  We study 1+1-dimensional theories of vector and hypermultiplets with (4,4)
supersymmetry. Despite strong infrared fluctuations, these theories flow in
general to distinct conformal field theories on the Coulomb and Higgs branches.
In some cases there may be a quantum Higgs theory even when there is no
classical Higgs branch. The Higgs branches of certain such theories provide a
framework for a matrix model of Type IIA fivebranes and the associated exotic
six-dimensional string theories. Proposals concerning the interactions of these
string theories are evaluated.
