New N=1 dualities from orientifold transitions. Part I. Field Theory

We report on a broad new class of N=1 gauge theory dualities which relate the worldvolume gauge theories of D3 branes probing different orientifolds of the same Calabi-Yau singularity. In this paper, we focus on the simplest example of these new dualities, arising from the orbifold singularity C^3/Z_3. We present extensive checks of the duality, including anomaly matching, partial moduli space matching, matching of discrete symmetries, and matching of the superconformal indices between the proposed duals. We then present a related duality for the dP_1 singularity, as well as dualities for the F_0 and Y^{4,0} singularities, illustrating the breadth of this new class of dualities. In a companion paper, we show that certain infinite classes of geometries which include C^3/Z_3 and dP_1 all exhibit such dualities, and argue that their ten-dimensional origin is the SL(2,Z) self-duality of type IIB string theory.