Braided Tensor Categories related to $\mathcal{B}_p$ Vertex Algebras

Understand

The $\mathcal{B}_p$-algebras are a family of vertex operator algebras parameterized by $p\in \mathbb Z_{\geq 2}$.

• They are important examples of logarithmic CFTs and appear as chiral algebras of type $(A_1, A_{2p-3})$ Argyres-Douglas theories.
• The first member of this series, the $\mathcal{B}_2$-algebra, are the well-known symplectic bosons also often called the $\beta\gamma$ vertex operator algebra.
• We study categories related to the $\mathcal{B}_p$ vertex operator algebras using their conjectural relation to unrolled restricted quantum groups of $\mathfrak{sl}_2$.