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

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We propose a method to challenge the calculation of genus-g, bulk n-point, b-boundary, c-crosscap correlation functions with x boundary operators Fg,n,b,cx in two-dimensional conformal field theories (CFT2). We show that Fg,n,b,cx are infinite linear combinations of genus-g, bulk (n + b + c)-point functions Fg, (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′).