The linear property of genus-g, n-point, b-boundary, c-crosscap correlation functions in two-dimensional conformal field theory

We propose a method to challenge the calculation of genus-g, bulk n-point, b-boundary, c-crosscap correlation functions with x boundary operators F(g,n,b,c)(x )in in twodimensional conformal field theories (CFT2). We show that F-g,n,b,c(x),care are infinite linear combinations of genus-g, bulk (n+b+c)-point functions F-g,F-(n+b+c), and try to obtain the linear coefficients in this work. We show the existence of a single pole structure in the linear coefficients at degenerate limits. A practical method to obtain the infinite linear coefficients is the free field realizations of Ishibashi states. We review the results in Virasoro minimal models M(p, p ') and extend it to the N = 1 minimal models SM(p, p ').