4d SCFTs from negative-degree line bundles

We construct 4d $\mathcal{N}=1$ 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 $\mathcal{N}=1$ 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 $n$.