  Motivated by the connection between 4-manifolds and 2d N=(0,2) theories, we
study the dynamics of a fairly large class of 2d N=(0,2) gauge theories. We see
that physics of such theories is very rich, much as the physics of 4d N=1
theories. We discover a new type of duality that is very reminiscent of the 4d
Seiberg duality. Surprisingly, the new 2d duality is an operation of order
three: it is IR equivalence of three different theories and, as such, is
actually a triality. We also consider quiver theories and study their triality
webs. Given a quiver graph, we find that supersymmetry is dynamically broken
unless the ranks of the gauge groups and flavor groups satisfy stringent
inequalities. In fact, for most of the graphs these inequalities have no
solutions. This supports the folklore theorem that generic 2d N=(0,2) theories
break supersymmetry dynamically.
