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

A bstract 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 F g , n , b , c x in two-dimensional conformal field theories (CFT 2 ). We show that Fg,n,b,cˣ F g , n , b , c x are infinite linear combinations of genus- g , bulk ( n + b + c )-point functions F g , ( 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 M ( p, p ′) and extend it to the N = 1 minimal models SM SM ( p, p ′).