| Summary: | Abstract We construct 4d N=1 $$ \mathcal{N}=1 $$ quantum field theories by compactifying the (2,0) theories on a Riemann surface with genus g and n punctures, where the normal bundle decomposes into a sum of two line bundles with possibly negative degrees p and q. Until recently, the only available field-theoretic constructions required the line bundle degrees to be nonnegative, although supergravity solutions were constructed in the literature for the zero-puncture case for all p and q. Here, we provide field-theoretic constructions and computations of the central charges of 4d N=1 $$ \mathcal{N}=1 $$ SCFTs that are the IR limit of M5-branes wrapping a surface with general p or q negative, for general genus g and number of maximal punctures n.
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