Gorenstein $T$-spread Veronese algebras

Let $S=K[x_1, x_2, \dots, x_n]$ be the polynomial ring in $n$ variables over a field $K$. We fix integers $d$ and $t$. A monomial $x_{i_1}x_{i_2}\cdots x_{i_d}$ with $i_1\leq i_2\leq\dots \leq i_d$ is $t$-spread if $i_j-i_{j-1}\geq t$, for any $2\leq j\leq n$. Let $I_{n,d,t}$ be the ideal generated by all $t$-spread monomials of degree $d$ and let $K[I_{n,d,t}]$ be the toric algebra generated by the monomials $v$ with $v\in G(I_{n,d,t})$. This generalizes the classical (squarefree)Veronese algebras. The aim of this paper is to characterize the algebras $K[I_{n,d,t}]$ which are Gorenstein.