Twisted affine Lie superalgebras and integrability

A twisted affine Lie superalgebra is either a twisted affine Lie algebra or of one of the types X=A(2m−1,2n−1)(2) (m,n≠0, (m,n)≠(1,1)), A(2m,2n)(4), A(2m,2n−1)(2) or D(m+1,n)(2) (m≥0,n>0). It is known that irreducible integrable highest weight modules over a twisted affine Lie superalgebra of type X do not exist if m≠0. In this paper, we show that nonzero level irreducible integrable finite weight modules over a twisted affine Lie superalgebra of type X do not exist if m≠0.