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We discuss supersymmetric surface defects in compactifications of sixdimensional minimal conformal matter of type SU(3) and SO(8) to fourdimensions. The relevant field theories in four dimensions are N=1 quiver gaugetheories with SU(3) and SU(4) gauge groups respectively. The defects areengineered by giving space-time dependent vacuum expectation values to baryonicoperators. We find evidence that in the case of SU(3) minimal conformal matterthe defects carry SU(2) flavor symmetry which is not a symmetry of the fourdimensional model. The simplest case of a model in this class is SU(3) SQCDwith nine flavors and thus the results suggest that this admits natural surfacedefects with SU(2) flavor symmetry. We analyze the defects using thesuperconformal index and derive analytic difference operators introducing thedefects into the index computation. The duality properties of the fourdimensional theories imply that the index of the models is a kernel functionfor such difference operators. In turn, checking the kernel propertyconstitutes an independent check of the dualities and the dictionary betweensix dimensional compactifications and four dimensional models.

Flavored surface defects in 4d N=1 SCFTs