In the first part of this Letter, we analyse the supergravity dual descript
ions of six-dimensional field theories realized on the worldvolume of (p, q
) five-branes (OD5 theory). We show that in order for the low-energy gauge
theory description to be valid the theta parameter must be rational. Irrati
onal values of theta require a strongly coupled string description of the s
ystem at low-energy. We discuss the phase structure and deduce some propert
ies of these theories. In the second part we construct and study the superg
ravity description of NS5-branes with two electric RR field, which provides
a dual description of six-dimensional theories with several light open D-b
rane excitations. (C) 2000 Published by Elsevier Science B.V.