Conformal super Virasoro algebra: matrix model and quantum deformed algebra

Abstract

In this paper, we construct the super Virasoro algebra with an arbitrary conformal dimension $\Delta$ from the generalized $\mathcal{R}(p,q)$-deformed quantum algebra and investigate the $\mathcal{R}(p,q)$-deformed super Virasoro algebra with the particular conformal dimension $\Delta=1$. Furthermore, we perform the R(p,q)-conformal Virasoro n-algebra, the $\mathcal{R}(p,q)$-conformal super Virasoro n-algebra ($n$ even) and discuss a toy model for the $\mathcal{R}(p,q)$-conformal Virasoro constraints and R(p,q)-conformal super Virasoro constraints. Besides, we generalized the notion of the $\mathcal{R}(p,q)$-elliptic hermitian matrix model with an arbitrary conformal dimension $\Delta$. Finally, we deduce relevant particular cases generated by quantum algebras known in the literature.