Punctures from probe M5-branes and N $$ \mathcal{N} $$ = 1 superconformal field theories

We study probe M5-branes in N $$ \mathcal{N} $$ = 1 AdS 5 solutions of M-theory that arise from M5-branes wrapped on a Riemann surface. Using the BPS condition from κ -symmetry, we classify supersymmetric probe M5-branes that extend along all of AdS 5 and intersect the Riemann surface at points. These can be viewed as punctures in the dual N $$ \mathcal{N} $$ = 1 superconformal field theories. We find M5-branes that correspond to the two types of simple punctures previously studied in field theory. In addition, when the central charge is rational, we find a new class of M5-branes with a moduli space that includes two internal dimensions in addition to the Riemann surface. These new M5-branes have the essential characteristic of fractional branes, in that a single one at a generic point of its moduli space becomes multiple M5-branes at special points