Chiral Gauge Theories from D-Branes

We construct brane configurations leading to chiral four dimensional N=1 supersymmetric gauge theories. The brane realizations consist of intersecting Neveu-Schwarz five-branes and Dirichlet four-branes in non-flat spacetime backgrounds. We discuss in some detail the construction in a C^2/Z_M orbifold background. The infrared theory on the four-brane worldvolume is a four dimensional N=1 SU(N)^M gauge theory with chiral matter representations. We discuss various consistency checks and show that the spectral curves describing the Coulomb phase of the theory can be obtained once the orbifold brane construction is embedded in M-theory. We also discuss the addition of extra vectorlike matter and other interesting generalizations.