4d N=1 from 6d (1,0)

We study the geometry of 4d N = 1 SCFT's arising from compacti fi cation of 6d (1; 0) SCFT's on a Riemann surface. We show that the conformal manifold of the resulting theory is characterized, in addition to moduli of complex structure of the Riemann surface, by the choice of a connection for a vector bundle on the surface arising from flavor symmetries in 6d. We exemplify this by considering the case of 4d N = 1 SCFT's arising from M5 branes probing Z(k) singularity compacti fi ed on a Riemann surface. In particular, we study in detail the four dimensional theories arising in the case of two M5 branes on Z(2) singularity. We compute the conformal anomalies and indices of such theories in 4d and fi nd that they are consistent with expectations based on anomaly and the moduli structure derived from the 6 dimensional perspective.