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

Abstract

Abstract 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 $$ {\mathcal{F}}_{g,n,b,c}^x $$ in two-dimensional conformal field theories (CFT2). We show that F g , n , b , c x $$ {\mathcal{F}}_{g,n,b,c}^x $$ 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 $$ \mathcal{M} $$ (p, p′) and extend it to the N = 1 minimal models SM $$ \mathcal{SM} $$ (p, p′).

Keywords

• Conformal and W Symmetry
• Field Theories in Lower Dimensions