2000 character limit reached
The linear property of genus-$g$, $n$-point, $b$-boundary, $c$-crosscap correlation functions in two-dimensional conformal field theory (2309.07528v4)
Published 14 Sep 2023 in hep-th
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 $\mathcal{F}{g,n,b,c}{x}$ in two-dimensional conformal field theories (CFT$_2$). We show that $\mathcal{F}{g,n,b,c}{x}$ are infinite linear combinations of genus-$g$, bulk $(n+b+c)$-point functions $\mathcal{F}_{g,(n+b+c)}$, 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 $\mathcal{M}(p,p')$ and extend it to the $N=1$ minimal models $\mathcal{SM}(p,p')$.
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